So today I noticed that when i shift or when i accelerate, my shifter is pulling forward, what feels like at the bottom of the shifter, and there is a loud knock like there's two things hitting against each other. Is there potentially something wrong/broken/worn out/missing with my shift linkage or anything in that system?

thanks in advance!

 

check the linkage bushings under the car for wear

 

motor mounts good?

 

Yeah this is a sign of tired and or broken engine mounts.

 

^^^

I'm doing a swap into my CRX which did the same thing you described, when I pulled off my mounts, my drivers side was holding on by a sliver of rubber, and my passenger side trans mount, the rubber fell out, front mount was fucked, the only one in decent shape was my rear because I had replaced it with a mount filled with polyurethane.
TAKE IT FROM ME UNBOLT AND CHECK YOUR MOUNTS!