Yes. That would be wise. You will be in J1 until you carry its responsibilities. Your TPS will be a backup plan.

Yes. That should work. If your employer sponsors, you are good. You need to take in mind that GC process is for future and that status is only when you have green card in hand or your i-485 is pending. The only catch is what if TPS status terminates when you have already started Green Card process whether at labor or I-140 stage, after applied I-485 should be ok. You need to go to status that let's you work i.e. H1B. Depending on when this happens you might be able to file with your current employer or new employer. Green Card process can take anywhere from 1/2 years to 3/5 years start to finish. If you have continued TPS stauts during that period you would be ok.

Tor those ( TPS holders) who have married U.S. Citizens, or have a citizen child over the age of 21, or those who have a job willing to sponsor them, you are eligible to apply for adjustment, at least without any problems such as false claims of citizenship, certain criminal convictions, or other grounds for inadmissibility or removal.
http://bgimmigration.com/2014/01/12/i-have-temporary-protected-status-tps-can-i-get-a-green-card/