AP Exams

Will credit earned from AP exams that I’m taking this May be eligible for transfer credit going into my fall application?

That would be up to the transfer policies of the school(s) you are interested in. Some schools only take AP as transfer credit IF 1). it is recognizably AP, 2). it is assigned a designated course that it replaces, 3). the number of credit hours it is worth is denoted. So, for some schools, as long as you can get your AP credit on your college transcript, they can include it as transfer credit.
Again, you would have to check with individual policies. What schools are you interested in?

I applied to UCSB and UC Berkeley. I’m taking two ap tests in May that are required for my major. I’m wondering if the credit I earn can be used for my major prerequisites and my required 60 transferable units. Again I applied for fall of 2015.

You can only use 6 AP exams that you got a 3 or higher on for transfer credit. One caveat is that they have to be for English, math, another humanities class, a social science, or a biological/physical science. More likely than not, though, most of the exams they accept are ones you took.