The stock bore on the B18a1 and B16 are the same. So feasibly, yes I believe you could. But there are a few problems that I could see arising:
1) if you're rebuilding the engine, it's probably got a lot of miles on it. A simple hone might not be enough to clean up the cylinder walls, you might be forced to bore it over the stock bore, rendering the stock pistons (and the B16's) useless.
2) Wrist pins for the B16 pistons may be slightly different than the B18's. I'm not too sure because I have never done this exact build.
Higher compression does not necessarily mean you will need bigger injectors. Have the car tuned after the build and see where that puts you.
Are you talking about a crank out of a 99 Integra LS? If your engine is a B18A1, then yes it will.
I'm almost positive the 90 Integra LS came with a B18A1, but it could have been a ZC. If it's a ZC, then no you can't use b16 pistons or the crank out of the 99. You have a completely different engine if that is the case.