I think the same rules apply. You can exercise but you'll owe taxes and can't sell any shares to cover the tax.

I don't know details on stock options, but for RSUs, my understanding is that it works like this: your signing bonus and part of yearly perf bonus is in equity. Signing bonus matures in four years, incrementally. 25% vests at the end of 1st year, the rest vests incrementally by month. Perf bonus vests in 1 yr. Once a RSU vests, it's yours. If you leave the company before a RSU vests, you lose it.

At IPO, RSUs get converted into stocks, however, there's a restriction that you can't sell them for 1 year from the IPO date. Tax obligation is handled by subtracting a portion of the units, rather than by paying out-of-pocket.

No, you have to wait the year.