If you have a 7 speed cassette, and not a freewheel, it most likely already has an adapter spacer. I don't remember seeing 7-speed only freehubs except for 135mm MTB hubs.

Derailers are not speed specific, but they are system specific, and it's not always obvious what is compatible with what, and I couldn't tell you what yours is because I've never heard of a spectro rear.