The term active may be a bit of a reach. I loved my Acuras when I had them but really have zero desire for another Integra. Got in to this RWD world and haven't looked back. Have an M6 that has become quite the fun car.
Are you going to sleeve it? Get a new bottom end? Need new crank? If it was ran without oil there is a chance the bottom end is toast and you will need a new bottom end. If you are just going to throw parts at it then you will need to put proper pistons and rods in the proper block. Most of you...
Yes there is a stamped number on the head. If I remember correctly the b16 will be a PR3 stamp. Lots of B series parts are interchangeable. Guess it depends on what you are trying to buy.
Sounds like something was maybe bypassed at some point. Distributor rotor. Sits under the cap and held on by one screw if I remember right. Cap and rotor are cheaper than a new dizzy altogether
Sounds like you are fine. There is always the chance another B-series trans went in the car before you received it. B16 has very short gears.
Check out some honda gear ratio calculators.
Should be good to go. Sounds like you are replacing with and OBD 2 head.
https://honda-tech.com/forums/acura-integra-6/quick-write-up-differences-b18b1-heads-pr4-p75-2412502/