Size & demography
The Galactic Empire in Seldon's day nominally ruled over the entire Milky Way galaxy, spanning "billions of suns" (Mayors, 3) and "nearly twenty-five million inhabited planets" (Psychohistorians, 1). According to Seldon, it has a population of "nearly a quintillion human beings" (Psychohistorians, 6).
Of the post-imperial states, it is known that the Kingdom of Anacreon spans twenty five star systems with thirty one or more inhabited planets and a total population of nineteen billions (Mayors, 6), while the Korellian Republic embraced "some half-dozen stellar systems" (Merchant Princes, 1).
In the period explored, the Foundation grows from a single planet to a minor galactic state with effective control over the Four Kingdoms (Anacreon, plus its competing neighbors of Daribow, Konom and Smyrno) and Askone. Though no specifics are given, extrapolation from the known demographic figures of Anacreon suggests the Foundation to have a population of high tens to low hundreds of billions spread across high tens to low hundreds of planets in Mallow's time.
-Planetary populations of interest
Trantor, Imperial capital and throneworld, has a stated population "well in excess of forty billions" (Psychohistorians, 3) at the beginning of the thirteenth millennium. However, since it is also an ecumenopolis "75.000.000 square miles in extent" (Psychohistorians, 3), this figure suggests extremely low population densities.
Terminus, capital of the Foundation, was first settled by a hundred thousand colonists (Psychohistorians, 6). Fifty years later, the population was "a good million" (Encyclopedists, 3). Approximately one century after this, there were "five million homes on Terminus" (Merchant Princes, 14), which suggests populations in the tens of millions.
Industry
We are given nothing useful about Imperial industrial capacity, except for the fact that Trantor is an ecumenopolis and that it builds big ships. However, since we aren't given either useful timeframes or the amount of resources devoted to either effort, nothing much can be done with either.
For the Foundation, the closest to useful data is the Anacreontian militarization incident, though my initial figures have to be revised after some highly relevant observations in SD.net about the actual meaning of "half again". So....
*Anacreontian militarization (revised).
The battlecruiser Wienis had 150% the volume of the Anacreontian fleet. That fleet was more or less built from scratch in the roughly thirty years that followed the emancipation of Anacreon from the Empire. Note that this was not wartime production and that the Foundation hadn't yet completely rebuilt the Imperial energy production network.
The Wienis was two miles in length. Although we don't know anything about its volume (other than all descriptions of Imperial warships suggesting that they are massive and colossal), I have used the volume of eight Imperial Star Destroyers (ISD), which should be an adequate benchmark within an order of magnitude in either direction.
9E7 m^3 * 8 = 7.2E8 m^3
7.2E8 m^3 * 2/3 = 4.8E8 m^3 (estimated production over thirty years)
4.8E8 m^3 / 30 = 1.6E7 m^3 (estimated yearly production)
Since Anacreon was just a small fraction of the Galactic Empire.
Using the Anacreontian figures for the Empire in a per planet and per capita basis we get that:Following closely the boundaries of the old Prefect of Anacreon, it embraced twenty-five stellar systems, six of which included more than one inhabited world. The population of nineteen billion, though still far less than it had been in the Empire's heyday was rising rapidly with the increasing scientific development fostered by the Foundation.
Estimated Galactic Empire production (per planet): 1.6E7 m^3 * 800,000 (Anacreon is estimated to have ~30 planets) = 1.28E13 m^3 (~140,000 ISD sized warships a year).
Estimated Galactic Empire production (per capita): 4.8E7 m^3 * 5.25E7 (Galactic population/Anacreontian population) = 8.4E14 m^3 (~9300,000 ISD sized warships a year).
Communications
The technology appears to be the same for all factions in the setting. Mention is made in the text of "wave", "hyperwave" and "ultrawave" (Mayors, 6-7), as well as "sub-ether" communications (Traders, 1). From context, wave appears to refer to communication based in EM effects, such as radio, while hyper and ultra appear to be one and the same with one being noted to propagate "through hyperspace" (Merchant Princes, 17) and the other having "instantaneous speed" and a range of "light-years" (Mayors, 7).
Sub-ether might be a third designation for the same kind of supraluminal comms, but all we are told is that it "cannot be trusted" as a way of delivering confidential information (Traders, 1).
In Imperial times, these techologies were widespread and this made possible for a student of a distant world to have seen Trantor many times in "hyper-video and tremendous three-dimensional newcasts" (Psychohistorians, 1). After the Fall, even the singularly backwards state of Askone could still be contacted by individuals in a different star system for negotiation (Traders, 2) and, in Mallow's time, the Foundation could broadcast in real time 3D imagery to "private 'visors in almost every home of the Foundation's planets" (Merchant Princes, 14).
Space travel & spacecraft
Perhaps simply because of a greater availability of resources, the Empire is shown to build spaceships in a much larger scale than the Foundation. The Wienis, a three hundred years old battlecruiser, was a "two-mile-long ship" (Mayors, 7); Gaal Dornick went to Trantor in a passenger ship carrying "thousands of passengers" (Psychohistorians, 2); and the warships gifted to the Korell Republic by the imperial viceroy of the Normannic Sector are stated to be "like whales to a minnow" in comparison to a Foundation tradeship (Merchant Princes, 17).
In the Imperial side of things Seldon's day, Trantor was daily supplied by "fleets of ships in the tens of thousands" (Psychohistorians, 3).
Meanwhile, in the Foundation side of the coin and talking about Mallow's time period, the half dozen star systems of the isolationist Korell Republic were visited by "better than three hundred" Foundation tradeships in a single year (Merchant Princes, 4). Loss of three ships was a concern only in as much as it represented the possibility of an enemy armed with nuclear technology (Merchant Princes, 1) and the destruction of up to six vessels was regarded as "just a scratch" (Merchant Princes, 18).
-Slower-Than-Light travel
Nothing of note is mentioned concerning slower than light engines, except for relatively vague statements that give the impression of hours being spent in a STL approach to the destination planet after completing the FTL transit.
-Faster-Than-Light travel
The only known method of practical interstellar travel is the Jump, an instantaneous journey through the supraluminal "region" known as hyperspace, during which it is theoretically possible to "traverse the length of the Galaxy in the interval between two neighboring instants of time" (Psychohistorians, 1). In practical terms, however, hyperspace travel is a lot more involved than this and Jumps a lot shorter, so that travel between two distant star systems follows multi-Jump routes. This is what made it possible for Terminus to be isolated from the rest of the galaxy when the province of Anacreon declared independence and became the Four Kingdoms.
Weapons Technology
-Handheld Weaponry
Slugthrowers are not unknown in the galaxy and seem to have spread in the Periphery, during the Fall. Hunting for the Nyakbird of Anacreon is stated to involve use of one type called the "needle gun" (Mayors, 3) and Hober Mallow was surprised to recognize the barrel of the handguns used by the Commdor's bodyguards as nuclear, rather than those of a "explosive projectile weapon" (Merchant Princes, 3).
In regards to energy weapons, generally called "blasters" in-universe, they are shown to have adjustable levels of firepower, from an "almost burnless minimum" (Merchant Princes, 11) to higher levels that can result in a human "head blown into nothingness" (Mayors, , if fired from point blank range.
-Naval Weaponry
Little is known about the weaponry used in capital scale warfare. During the first Seldon Crisis, Hardin mentions that it would be convenient to have "a few great big siege guns fitted for beautiful nuclear bombs" (Encyclopedists, 3), the Imperial battlecruiser is described as having "nuclear blasts capable of blowing up a planet" (Mayors, 2), and nuclear explosives are noted to be "usual" in "light-armed" Foundation tradeships (Merchant Princes, 1 & 4), during Mallow's time. Other than this, we only have the vaguest mentions of starships being armed, having several guns and so on.
-Forcefields
Defensive forcefields were widespread technology in the pre-Fall Empire. A three hundred years old Imperial battlecruiser is noted to have a shield that "could take a Q-beam without working up radiation" (Mayors, 2), which is apparently supposed to be highly impressive. It is also mentioned that the Empire developed vast shields capable of protecting "a city, or even a ship" (Merchant Princes, 10) and, according to Mallow, "an entire world" (Merchant Princes, 18), but not super-miniaturized man-portable shields for "one, single man" (Merchant Princes, 10).
Meanwhile, the Foundation tradeships have as standard "force-field defenses" (Merchant Princes, 1) that supposedly can only be defeated with "more nuclear power" (Traders, 2 & Merchant Princes, 1). Moreover, their efforts in technological miniaturization allowed them to develop man-portable forcefields as early as Hardin's administration (Mayors, , with the technique being sufficiently developed in Mallow's time that they had also developed a type of blasters "especially designed to pierce" such shields (Merchant Princes, 11).
Other
Though still interesting enough to deserve some commentary, certain technological capabilities of the factions in the setting have little immediate usefulness in a conventional versus scenario and therefore only get cursory mention here.
These include, for example, the Empire's gravity manipulation technology (limited in the period to glorified lifts), the Foundation's economically non-viable transmuters, Mallow's atomic tools, the oft-mentioned lifelike holographic tech, the intriguing mention of teleportation or the anti-spy devices that pop up a couple of times.
Well, that's about it for Foundation. Next, supposing that I continue past this point, would be Foundation and Empire.
See you around.