Is parking available?

There is a parking lot across from BAM by the Whole Foods store, Ashland street side. It might be expensive.

depends when you go but I always find street parking at 6/7pm

Yes, on street parking is available also. There's also construction in the area. BAM is steps away from the 2,3,4,5,B,D,G,N,Q,R, W* & LIRR

There's a garage close to BAM, managed by Park Kwik (300 Ashland Place)

No. They do have an official David Byrne bike rack tho.