answers
The cylinder head is identified on the casting, on the left side around/under intake ports 4-5. It's been a while since I've looked so my memory is a little vague about this point.
The block number is stamped on a flat spot on the rear of the engine near the hole used for ignition timing. It's likely covered in dust or crud depending on how recently the engine swap was done and how clean your engine is. Mine weeps oil at the head/block joint, a fairly common issue, so it's filthy and I couldn't see the number stamp without some cleaning. It's not easy to get at, either.
By reputation, Sanden rotary compressors are quite good. Others will have to chime in as to what cars this compressor was installed OE, but it sounds like you are going to buy a new compressor. It may be a problem to assemble components to completely replace the supposedly anemic original AC on a coupe, but it has been done. HC-134 being less efficient compared to Freon, you may want to change the evaporator and condenser. You will always change the receiver/dryer if the system is old and has been opened.
It seems to me that there are LOTS of AC shops around, though most simply want to hack out a $40 recharge. As with anything automotive, there are also some (quite a few?) sharks out there waiting to tear off both arms and a leg of your wallet. Suggest you collect the experiences of others in your area before you commit to a shop.
