Ps3 – Does the Logitech F710 work on the PS3

The aim assist is available only in the campaign not in the multiplayer. The way it works is that it helps you 'snap' to the target nearest to the reticle while aiming down the sights. So maybe that snapping action is throwing you off. You can disable it and try.

It takes time to transition from PC to controller and while keyboard and mouse maybe more accurate, you will get used to the controller soon enough.

Now to answer the other part of your question, there are some non-standard controllers (read cheats) that provide extra functionality like this one. But you can't use a keyboard and mouse to play regularly.

Don't be too afraid to open it up. I've had to open mine a couple times to replace thumbsticks destroyed by my son. iFixit has some great guides for replacing almost every internal controller component. The hardest part is getting the pieces that fit between L1/L2 and R1/R2 back in and secured.