MacBook Pro fuzzy screen and freezes on startup at the Apple logo with half progress bar

I would say that you have a dying/dead discreet GPU, as that's a known problem with your model of MacBook Pro. Booting into safe mode may be doing something to help your GPU (I have an Xserve with a confirmed dying GPU that boots in safe mode but not without it) so it boots properly. I would highly recommend getting your MacBook Pro replaced as soon as possible via the Apple program. I would suggest you run Apple Hardware Test and verify that your GPU is dead/dying, but this may not be possible given your current state. Similarly, you can run a GPU stress test program like Unigine Heaven and see if your GPU quits.

The only thing I find interesting is your previous shutdown reason: overheating. According to this post, shutdown code -3 is temperature based. That's strange, but not impossible.

In any case, seeing if you can get your computer replaced probably isn't a bad idea since it's pretty likely your GPU is dying. Go to an Apple store, explain the issue, and they'll probably give you a new computer.

Try Resetting the SMC (if you haven't already, and see if that changes any of the mentioned behaviors)

1. Shut down the Mac.
2. Plug in the MagSafe or USB-C power adapter to a power source and to your Mac.
3. Using the built-in keyboard, press Shift-Control-Option on the left side of the keyboard, then press the power button at the same time.
4. Release all keys, then press the power button again to turn on your Mac.

The SMC or System Management Controller can require a reset and exhibit similar symptoms when malfunctioning. If this doesn't help, I can only suggest there may be hardware damage somewhere or possibly latent water damage side effects manifesting themselves.