1. No, you can't pair 10-speed shifters with 9-speed cassettes- the RD is probably fine though.
2. Yes, Shiftmate might work fine - you'd likely need new cables and stuff but if you're swapping derailleurs you probably would do that anyway.
3. You could also get a new 10-speed cassette instead of using your existing 9-speed - that'd probably be a better option if you're going to leave the Alpine gearing on after your Brevet (chappeau btw)