We use Exedy replacement clutches at my shop and have never had a problem in many years with them. And yes, the Exedy replacements are for a wide range of civics- kind of a one size fits all replacement. If you do replace your clutch, get your flywheel machined to ensure a flat and new surface. Even if its already flat, there could be "hot spots" on it that would cause chattering down the road.
All "hydrolic" clutches (vs cable clutches) are self adjusting. Honda recommends never to adjust the clutch master push rod, as it should be pre-set from the factory. If its been mis-adjusted, it may not be able to fully disengage the clutch, thus giving hard to shift symptoms. Should have some "free ply" at the top and bottom of the pedal travel. If it is misadjusted, it could wear things out faster in the clutch housing. So yes, it can "smoke" the face of the pressure plate and over use the throw out bearing. If the pressure plate has been in and out several times, the pressure plate can also create a warped "pressure"- due to the large center spring that hold pressure to the clutch getting fully flexed and unflexed if removed in an uneven pattern. Again, that would only cause a chatter upon engagement.
Great news about the syncros- if they are ok, and you install a new clutch and machine the flywheel, and still have the issue- then you have also narrowed it down to the hydrolic portion of the clutch system. Good idea also is to inspect the shift linkage for loose joints and worn bushings, as these things can change the alignment of the shifter input as its forcing things into gear.