Will a better webcam fix my dark video?

Partially, but a ring light is cheaper and more effective. Even the best webcam cannot create light that is not there. A $20 ring light plus your current camera beats an expensive webcam in a dark room.

Should I use the webcam mic or a separate microphone?

A separate USB microphone positioned near your mouth sounds dramatically better than any webcam mic. Webcam mics pick up room echo and background noise because they sit far from your face.

Best Webcams and Microphones for Better Zoom