Where are you located? If it's a 1992 it's not a US model water cooled 750 as they were oil-cooled, the 750Ws didn't make it here until 93. In 92 we got just the 600. Could be a Canadian model...or could be a 92 600 frame with a different motor since the frames were basically the same for the 92-93 600, 93-95 750 and 93-98 1100
1. I expected round headlights and this has a squareish headlight. Must be aftermarket
Not stock, not sure what it came off of, but you should be able to find a part number on it somewhere and google it.
2. I cannot identify the fairing, is it aftermarket? I need a rear cover for it but, not sure which one to get.
Looks like an Airtech Yosh front kit (with the headlight cutout and added) and possibly an Airtech SRAD tail kit, though I thought those were all one piece without a pillion?
3. The carbs are 36mm Mikunis (I measured the inside engine side bore). They don't seem to match the bike. The inner carbs are spaced to the boot but the outside ones don't. The bike has a push/pull throttle cable and these carbs don't have that type of linkage.
Stock (California spec) was 36mm, but with push/pull linkage. Non-California was 38mm. Perhaps off an earlier oil-burner? not sure if they had push pull cables, though I'm fairly certain they did. The spacing issue could be the boots installed in the incorrect locations (they are specific), or the wrong boots since OEM parts are getting harder to find.
4. What carbs would work on this bike? (Size, year, model)?
Whichever carb you fit and jet. You can use the Mikunis in 36 or 38, some go with the flat slide TMs, there are others available as well if you search.
5. What carbs would be best?
The ones that work lol...see above
6. There is a Vance & Hines ignition pack on the bike. Is that stock?
If it has a brand name other than Suzuki on it...it's not stock
7. Would an engine from a 2001 GSXR fit this frame without cutting the frame? I can make brackets and do the wiring and what is necessary if it is possible and a good idea.
No. Two different generations of bikes. The biggest difference is that the later motors are suspended, where the W motors sit in a cradle. You would end up reworking the entire top half or the frame just to fit the airbox/tank/carb body/injectors, as well as clearance issues with exhaust, radiators, etc. Cheaper to buy an 01 frame to put the motor in.