N aim assist in State of Decay on PC

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.

Mass Effect 3 does not support any other input than mouse and keyboard on the PC, so there is no official way to use an Xbox 360 controller on the PC. See for example this thread on the official forums where a Bioware employee states that the inability to use a controller is intended.