You can't change the alpha group significance test because a normal distribution isn't always best for alpha diversity. I'm guessing you have relatively small sample sizes? I guess one of the questions I should have asked sooner is if you rarified your data?
Your beta diveristy questions have been addressed before in multiple threads, those are compiled into the Frequently Asked Question Post.
I think you'll probably find your answers there, but if not, please come back and ask more qustions!