So, I recently got UFO: Aftermath and started playing it. I then noticed there was some patches for the game so I downloaded them, whenever I tried to install them such as 1.2 it says that UFO: Aftermath isn't installed on my computer. I had been experiencing a bug of somekind in one of the areas and in patch 1.2 it says it fixes it.

How do I install patches for the game? Because as far as I know, I can't since the patches say "It's not installed"

GOG games are already full patched with official ones.

I am wondering about the "total patch" v1.4 here:
http://www.strategycore.co.uk/files/english-1.4-total-patch/

I picked up a mod from here on the recommendation of a LP. He also mentioned fan patches beyond the official one. Is this it?

Nope, this is the last official.
AFAIK there is no fanpatch for Aftermath, there are only for AS and AL.

Maybe I misheard the LP. I did also listen to LPs for the sequals so I may have picked it up from there. There is a "Combo Mod" out for Aftermath though that I supposedly really good and fixes some lingering issues. I installed it right away so dunno how much it has improved or not :-D