#1
I have seen several videos and lessons about how to sweep. Lot of them don't mention muting while sweep picking so I did some research. I found something about using the thumb but I don't understand perfectly and I can't mute the strings in the way I want.

May you explain this for me in a good way or refer to a lesson/video lesson?
(Muting when sweep picking)

Thanks UGs!
#3
Use your palm and finger/hand flesh from your left hand in addition to the usual picking hand muting. Also as the guy above said, doing hte sweeps too close to the bridge can make it more difficult, so try out having your picking hand closer to the fretboard.
And of course, make sure to avoid letting the the strings ring together by not lifting the fingers quickly enough.
But it's all about practice, and you'll find your own way of doing the sweeps after a while.