Ok so i want to put the spare rim on and take off another rim because its tread is worse then the others.

The tyre on the rim though is bigger then the current rims slighty but is offset by the current size of the rims as they have low profile tyres.

Will this damage my car in any way shape or form since it is slightly larger?? Is it a problem on long trips?

Thanks!

Dont do it. Tyre dimensions on the same axle should be the same size. Should be
OK as a spare in an emergency. Dont skimp on tyres so go get new ones rather than botching it