Apple Internal Hard Drive Error So long story short, my iMac was working perfectly fine and I just decided to restart it because the fan was loud, it made a weird noise and now it keeps taking me back to either reinstall my macos, disk utility, and time machine. 

I try clicking my Macintosh HD but it isn't even showing even after running first aid it says that "it has failed, is possible back up data on this volume". I also went on reinstall macos but does not show my Mac HD in there ... Any solutions ?
You really need to put this Mac in target disk mode and connect it to another Mac - or you can accomplish the same things buy installing a fresh copy of Mac OS on a USB external drive and booting that.

Once you're running normal Mac OS on another drive, you can run SMART Utility to see if your drive is having a hardware failure. If it is, time to replace it. If it's not, you should run a good drive repair utility like DiskWarrior. Unfortunately, while Apple's Disk Utility technically performs these functions, it's fairly useless at both.