In terms of trims, CX < DX < EX < LX in terms of features, while VX(92-95)/HX(96-00) are kindof off to the side as being upgrade for super economy, while Si is an upgrade for performance.
EH2 means that the chassis is either a CX, DX or VX trim. From the pictures it doesn't appear to have power steering, but that doesn't narrow it down any. The air conditioning and power steering was an optional upgrade on any of those trims.
If it's a CX or VX, the stock tire size should be 165/70/13, while the DX would be 175/70/13.
If it's a CX/VX, it should have a super-tall transmission (=yay). The DX has a shorter transmission. You'll know once you get on the highway, because a CX/VX transmission with the correct tire size will run about 2250rpm at 65mph. A DX tranny with the right tire size will be about 2750rpm at 65. This isn't too bad though, I still get 35-40mpg with a 1.8L B18 engine in my car (which has worse aerodynamics) on the highway screaming down the road at 4000rpm.
All 92-95 Civics came wired from the factory as OBD1. There are 3 possibilities: (1) the new engine is running on an ODB1 computer not designed for it (possibly re-tuned so it's ok), and it's using the stock wiring, or (2) the new engine has a
jumper harness converting the wire harness to OBD2 right before the ECU, which would *probably* cause it to throw a CEL (check to see if the CEL bulb is still in the cluster or working, it should flash when you start your car) or (3) the entire car wiring has been replaced, which is pretty unlikely.
As a side note, I believe OBD0 and OBD1 share the same distributor and injectors, and OBD1 and OBD2 shares an alternator. It's possible to mix and match them with jumpers (converters) though. If scenario 1 or 2 is correct, it's likely that the OBD2 engine is using the OBD1 injectors and distributor from the old engine so they would fit on the harness. This shouldn't be a concern as the computer is what counts, but be aware when shopping for parts that you won't be shopping for the injectors/dizzy for a D16Y7. Definitely find out what computer you're running.
EDIT: Is it possible to borrow a tie rod tool from NAPA? I have another Civic that's in need of fixing and I don't want to spend $60 on the tool.