So i am trying to adjust the front derailleur limit screws and cable tension, but i can't get it to shift smoothly. It is struggling to shift the chain to the smallest ring, especially under torque, but when the chain finally shifts, it falls out between the smallest chainring and the frame. Any ideas on how to fix this since it makes no sense?
Although I suspect that this may get you into more trouble.....
Your front derailleur has a lot more adjustments than the rear. This is to account for different sized chain rings. Make sure that the height and the alignment of the derailleur clamp haven't changed.
To rule out the possibility that the cable or the mechanism isn't sticking due to grime build up remove the cable from the cable clamp altogether and test that the mechanism snaps back. If it does adjust your limit screws from there.
have you tried turning the small chainring around? The small chainring might be fitted back to front. If you look, the teeth are not in the middle of the ring. If you got it with the wrong side facing out, it can cause this issue. Search the web for the correct orientation for your chainring. Good luck!