I thought the alpha figs were going to be compatable with normal heroclix. I bought a few and I was looking at their cards. The powers are very different from regular clix. So if someone were to play alpha figs in a regular tournament would they use the power as it's described on the card or would they use the normal power?

For example....Gordon has a yellow square on his first defensive clix. The alpha power gives a +1 to all friendly adjacent figs. Would we use that or use defend?

In standard (ie non-Alpha) Heroclix games you ignore the Alpha character cards except for the keywords.

What he said.

Are they then leagal for restricted tournaments?

Yes Batman Alpha pieces are legal for restricted events.