1. The ffmpeg does not ruin After Effects (assuming you're referring to the product here, not something else). Now, I've never used After Effects but quite a few others do and none of them have had any problems with it afaik. There's probably something else wrong with your workflow. If you describe it in detail, someone who does use AE might be able to help you.
2. You'll be missing out on an absolutely constant framerate and all the other rendering modes if you don't use the builtin rendering but some screen recorder, make sure you're fine with that. If so, press F1.