Hi Mark, we start slow then speed up over time. I think it is more important to play it correctly at a slow speed than to play it incorrectly at the normal speed. (However, sometimes it is fun to see how fast we can go.)
I would not recommend using a mute. Part of playing the fiddle is learning how to produce pleasant notes. You can’t do that if you are muting your instrument. I would only use a mute if I were trying to keep others from hearing me.