What is the need to change the chainset or go 7 speed ?
The STX-SE is many leagues above what you have on there, and yes you'll need a 68-110mm bottom bracket for it.
The one fitted will be ~68-122 from the look of it's profile.
If you want to go 7 speed then Just get a cheap 7 speed 130mm wheel. Old Deore DX crop up often for not a lot and can be found in that measurement as well as others, but you'll be looking for turn of the 90's era really. but get them to measure. Though you'll have little problem fitting a 135mm setup in there and often easier to find now.
Get a full wheel it's cheaper.
You'll then need the shifters as well.