I haven't done a system repair before, and I'm concerned that the process will alter / screw up my installed applications.
Will I have to reinstall any of my apps/programs, or does Windows 7 system repair leave them intact and untouched?
System repair only fixes system-related parts, it has nothing to do with the installed applications or programs.
Repair the system, only scan the system folder, restore the illegally modified system files to the default legal version, that is, only affect the system files. The user's personal files and installed software are not affected.
What are the system recovery options in Windows?
System Recovery Options: Guide for Windows Vista, 7, 8, 8.1 and 10