1. 650C wheels have an ETRTO/ISO diameter of 571 mm and the tires were specified in inch and fractional inch dimensions so the 26x3/4" implies they are 650C. Look at your tire sidewalls to see if they also say 571xXX. If so, the rims are 650C.
2. No ideas.
3. Measure the dropout width. Many late 7-speed bikes were spaced 130 or 128 so they will take any 8/9/10-speed wheel. 7-speed brifters are still available, mostly NOS RXS stuff, and 7-speed downtube shifters are too. 7-speed barcons are getting quite scarce. One work-around is the "8 of 9 on 7" approach (8 cogs from a 9-speed cassette fit perfectly on a 7-speed freehub) used with 9-speed shifters of any type.