For spreading fingers to make long stretches, I'd suggest working with two fingers at a time, at first, then add the third to create a "broken" triad (play 2 strings, then play the 3rd separately), and work on that until you can hold everything down at once. It's just a matter of time, patience, practice and persistence. Don't expect too soon, as our GW leader might say.
For the other questions, what is the specific video lesson you are working on? Which string set is causing the trouble? Are you using 3 adjacent strings working up the length of the neck?
Muting is a magic art. Both the left and right hand are involved and there are several types of situations and techniques for each one. But it is easy to overthink too much.
You really need to experiment to find out which combination of techniques work for your style.
I try to use left-hand mutes to keep unused strings quiet and use the right hand to control how long fretted notes ring (in combination with lifting off the fretting pressure). It may work for you to do it the other way around, or to always use both hands, or use different fingers, depending on which fingers are fretting or if you're playing open strings, too.
Again, patience and practice. Good luck and happy practicing!