Re-installing Mojave

I have been having problems with my iMac 21.5 late 2015 for a while now. One of the problems is the applications folder in my home folder is empty, but it is still in the side bar of the finder. The applications in the time machine have no entry signs.

I would like some guidance please. Could I copy the files I want to keep to an external hard drive or memory stick, re-install Mojave as if I was selling the Mac on, then copy the files back from the external hard drive. The question is would it work for me? Help will be much appreciated.