These questions don't relate to one another but I figured it'd be best to consolidate them into one thread rather than flood the forum with multiple.

1. I always play with my thumb on the back of the neck of the guitar, pointing towards the neck and slightly tilting upwards. I don't stress out over this since it's comfortable and works. However, whenever I bend a string, I always put my thumb over the neck to to help support my fingers as they perform the bend. This gets slightly annoying though. Say, for example, I was to play this:

Now, for everything but that one bend (7b9), my thumb would be at the back of the neck, only reaching over the neck for that bended note. Is moving my thumb around something I'm going to have to get used to? The reason I ask is because when people talk about finger strength and independence, I rarely see any mention of the thumb. Any input regarding the mobility of this finger and its role would be appreciated!

2. On another note, for string muting, say you have this:

To mute those strums, I'd simply loosen my fretting hand and let them rest on the strings for that deadened sound. But what about muting with the strumming hand? When does that come into play and how is it performed? Would you mute with your strumming or fretting hand here?

Sorry if these questions seem long-winded or awkward...just things I've been wondering. Thanks for any responses.
For the first thing: As far as I know, it's a bad habit a lot of people have (including me) and you either get rid of it or you don't. If you actually look around, you'll see tons of famous guitarists do that.

The second: When I have to mute the strings, I either mute with both the strumming and fretting hand, or just the fretting one. When I shift chords (and mute), then I use both, while if I only play 1 chord and have to mute between the strums, I only use the strumming hand.

I hope I helped a bit.
1- The correct technique for bending is to put your thumb over the neck. Don't worry about it, you're doing it correctly.

2-those xxx on the tab mean you play dead notes, like you're doing. Palm muting is done with the palm of your picking hand, and it's represented on tabs as a PM|------------- over the tab, meaning that when that symbology is present, you mute the strings, until it is over.
1. You're going to have to get used to changing thumb positions, after a while it just feels natural.
2. It depends on the sound you're trying to achieve but most often I'd mute with the fretting hand and the picking hand, with the picking hand palm muting.
Speed is a by-product of shut the fuck up.
1) thumb over the neck for bends is good, although in "classical" position the thumb points towards the ceiling, not the headstock.

2) you're doing it correctly. Strumming hand muting sounds different, think about palm muted punk riffs.
1- Some blues players that rely heavily on bending actually let it hang over the neck all the time. This also allows you to play hendrix style barre chords and more bass/melody freedom like a piano player. With regular barre chords you are pretty much stuck with the bass note for the bass

So I guess it depends on the style you want. In general thumb behind is probably more efficient for a lot of styles but the thumb over can open up some awesome possibilites

2- You can do it both ways. You can ease on the pressure like you do and it gives you a "chuck" sound or you can do it with right hand, slamming (gently) and strumming the muted strings, which sounds more like a clap. It's useful to learn to do it with right hand too in case you want to play open chords