B18A1 Acura Integra Motor

I'd say as long as you keep the psi at 7 or below. No guarantees, but the B18A1's stock parts are likely able to handle up to that much. The compression is perfect for boosting, though. If you're upgrading the pistons to deal with more psi, you'd want to upgrade all the other stuff too most likely. If something breaks down there, your whole engine could be destroyed by a rogue piece of metal ripping off of a connecting rod or something else.

The OEM crank is totally fine. You can do hundreds of horsepower on the stock crank without issue.

You probably want to get some decent connecting rods or at least ARP rod bolts. Aftermarket connecting rods like Eagle rods are pretty inexpensive and are a pretty good choice for building high powered aftermarket B-series engines.

The stock pistons aren't too high compression, which makes them decent for turbo. Depending on your goal and budget, you may want to consider forged low compression pistons, though. Wiseco makes some great pistons as do some of the other companies out there making B series parts. An aftermarket piston will take more abuse and will be better suited towards turbo.

If you're going with aftermarket pistons, I'd spend the extra $400 and get some Eagle rods while you're at it. Your build is going to be as strong as the weakest link.