Its really good that you are asking questions and then thinking of questions to answer from the answers given to you. I drove my instructor nuts with this stuff for a long time, until I started realizing that there are many questions in aviation that cant be answered in a "black and white" way.
I think it would really depend on how much you need to deviate for weather. If its a small 10 or 20 degree turn for a smaller towering cumulus cloud, then it probably wouldnt present much of a problem (to answer your conflicting traffic question, if you can see the weather you need to avoid, you can probably see and avoid other traffic in your vacinity). If you need to deviate a hundred miles off course for weather (without ATC approval, in the US), then you will most likely have some explaining to do.
Bottom line is, in an emergency situation, do what it takes for the safety of the passengers, crew and aircraft.
EDIT: I also wanted to add that in the US (Chicago Center specifically, since most of my Center experience is with them), you will almost always get your deviation for weather avoidance. Even on the busiest days, Ive heard them approve every request they got. Although 15 minutes later they shut down their airspace to any more incoming traffic and placed everyone outside in a hold. I heard quite a few upset corporate pilots that day......