Will reinstalling macOS delete my data and installed apps?
Reinstalling macOS from the recovery menu does not erase your data. However, if there is a corruption issue, your data may be corrupted as well, its really hard to tell. 

https://support.apple.com/en-us/HT204904

I will take this time to remind you that the time for backup is BEFORE you have an issue, so hopefully you have a Time Machine backup or Carbon Copy Cloner disk around.

To gain access to the disk depends on what model Mac you have. An older Macbook or Macbook Pro likely has a hard drive that is removable, allowing you to connect it externally using an enclosure or cable. Newer Macbook/Macbook Pros and iMacs make it much more difficult, as their SSDs are not removable or very difficult to remove. I recommend you review the step by step guides at ifixit.com to see if you are brave enough.

Otherwise, find a friend's Mac, and follow these Apple instructions to set your Mac in 'target disk mode' and allow the other Mac to access your files to copy them off. Again, the corruption might make this impossible.

https://support.apple.com/en-us/HT201462

Oh, and backup your computer!