In general for everyone reading - I would advise caution on the freewheel hunt! 7th gear may hit the rear stays as the wheel was built for 6 - you can get around this with an extra 2mm washer but you will also have to spread the rear stays a couple of mm every time you take the wheel out.
Seeing how you updated your bike, those wheels will take a 7spd freewheel as they were built for that purpose but for those that still have the bike above, you need to faff a bit.
As for square taper chiansets, the majority will be JIS so theres nothing to worry about unless you decide to fit Campagnolo. They still fit just not quite as far up the axle. But going back to your bikes original equipment, you may find your axle is too long just swapping over as is. You may find the chainset sticks out a bit.