Chances are good that the frame's rear dropout length and each hub's outer locknut dimension (OLD) are all 135 mm. but it doesn't hurt to check.

Yes, you can use a 4.5mm spacer and 7-speed cassette on the 8-speed freehub.

If I had two wheels and one had a cassette and the other a freewheel, I'd use the one with the cassette for MTBing since it's a stronger setup. If they both took a cassette, I might use the one without the spacer for MTBing (less dish, stronger wheel), depending on other characteristics of the wheels.

I'd also use a wider-range cassette for MTBing (11-32 or 34), assuming the RD can handle that large of a cog, which it likely can.

There's a chance that the positions of the cogs won't be exactly the same between both wheels, so the rear derailer's barrel adjuster and perhaps limit screws may need slight adjustment after swapping, but 7-speed is fairly forgiving of imprecision with its relatively wide spacing between cogs.