Fingers crossing will definitely slow down playing in the future. It sounds like what Charlie said, that you might be using too much pressure on your index finger, so when you go to move your hand down the neck it doesn’t move as easily and the fingers overlap. The sooner you can kick this habit the better, even if it means slowing things down to learn it a new way. I had a similar problem where I would use the flats of my fingers when playing power chords and everything dragged and it took me a while to relearn but it’s proper now. As far as the second point goes, Jak nailed it. I like to exercise alternate picking and improve it by turning on a metronome and just picking up and down and up and down on a single string with the tempo until I felt comfortable, and then when I felt comfortable with that range of motion I would add another string above or below and do:
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———1-2-3-4————————
———1-2-3-4————————
And I would just keep tacking on strings and go up and down the cluster of strings while alternate picking until I could comfortably do it. You can also turn that into a left-hand exercise as well by varying the fingers used, and going 1-3-4 or 1-2-4 or 1-2-3 or even 4-3-2-1 from time to time. I hope this makes as much sense in writing as it did in my head.