Do we get computer access during BCT and AIT? Do we get to use a phone?

The answer is no and no for BCT, AIT is pretty much just learning your job so you are free to do what you want on your own time for that. BCT is designed to be stressful and simulate war time conditions. Therefore you wouldnt have access to things like facebook in the middle of a fight or call home while getting shot at so therefore they wont give it to you there.