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Josh K.why would there be a conflict between psa and gai? for starters, how about the owners of gai learned the trade at psa, left to start a competing business and that competing business would like to take away all of psa's customers.
as to your first question, I have heard that psa tends to adhere to their grading standards very strictly when crossing both sgc and gai cards. I personally have no experience crossing cards into psa slabs.
I can say from personal experience that sgc will give cards slabbed by competitors a fair review as I have had several cards that were sent in psa slabs that were bumped up half a grade. Of course, Ive also had several that have been downgraded or, if I was unwilling to accept a lower grade, that failed to crossover.