- few year ago I was on students exchange, so I possess SSN - can I use it without taking a risk of being tracked?
Technically yes. In practice, no. SS Administration and INS are two different agencies. If CIA and FBI can hardly get on the same page I doubt SS and INS will. Except when someone blows the whistle, or there is a concrete reason for investigation.
- its easy to find a job on black market?
It may be, but it is still illegal.
- can I open bank account, take a lease and so on?
Bank account yes.
Lease, only if you have some financial backing or a decent job. Working under the table makes you ineligible.
- what other difficulties I may obtain?
If you use your SS number there will be a record of your income (if you use a bank), there may be records of services you buy (phone, gas, electricity) and some of those may haunt you if you get nabbed by INS as they might be a proofs of your immigration status as an illegal alien, or an alien working in the US illegally, possibly not filing your tax return.
If you can't get the work permit, I'd stick to helping out family or friends in exchange for room and board.
That's considered work too.