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The WH description changes to reflect the status of the WH. If it says its at 'verge of collapse' then you have less than 5% of mass left, if its at 'reduced' but not critical then its at less than 45%. If it says its 'reaching the end of its natural lifecycle' the WH has less than 4 hours worth of time left. The wormhole will visually wobble badly if its been hit hard.
Additionally, the description and name of the WH will give you an idea of where it goes and what can go through it.
'unknown space' - Class 1 - 3
Dangerous Unknown space - 4 - 5
Deadly Unknown - Class 6
As for wormhole mass calculations and limitations:
LINK
Class 1 - Cant take battleships but can be done solo in elite cruisers, or respectable battlecruisers. Various sleepers use webs, nos as standard.
Class 2 - Can take battleships and can be done solo by better battlecruisers or battleships.
Class 3 - These CAN be done solo but it is not recommended because now Sleepers use Scrams
Class 4 -Cannot be done solo, approximately 4 RR battleships required, more sleepers use scrams
Class 5 & 6 - No chance of being done solo, This is where caps are allowed to come into play and the sleepers have DPS to match capitals, all sleepers use scrams
Additionally, W-space has spatial effects on things inside it. Sometimes they can be good, sometimes they can be bad so if you go into a WH look up the locus signature and see what it does. The greater the class of W-space the greater these kind of effects hit you, so a C1 might boost your shields by 10% and lower your armor resists by -10% but the C6 will boost by 90% and nuke your armor resists by -90%.
Sleepers, always focus fire on single targets and they use the closest thing to an 'aggro' mechanic you might expect from things like Anarchy Online. They web, scram, neut, nos and do full Omni damage so you have to get ALL your resists up and relatively equal. They have sick resists on their armor but none on their hull and they can target, fire and fly at speeds far greater than most of their player ship equivelents. The one saving grace for now is that Sleepers are highly vulnerable to ECM and ALL ECM racials work equally as effective so ECM is the great force multiplier if you dont have the firepower or tank to kill them quickly.
Other than the sleepers themselves, you will have to deal with other players. Its going to take you time to run through a site and in that time if you take your eyes of scanners then a group of pirates can come in, scan you down and jump you. Thus only taking a ship you can afford to lose is strongly recommended, and with random people entering and leaving W-space that means the WH could collapse while your running sites so a probe launcher is mandatory if you want to get yourself out.
I really wouldnt recommend the CNR for soloing. Command Ship or Drakes are quite common for C1 - C3 solo running and wont cost as much to lose.