How should I do this?
This is a really stupid question, but I am afraid that I've been playing for months incorrectly.

I hold the pick between my thunb and the last digit of my index finger. When I hold it, I make what looks like an OK sign.

Is this correct? I feel really silly
Also, would I be considered anchoring if I generally rest the heel (I think that's the area below the thumb) near the bridge on the low E string? It isn't necessar for me to play that way, but I am most comfortable when doing that.
Thum and the side of your index finger is usually considered ok so don't stress Though when you say you're making an 'ok sign' are your fingers relaxed or tense??

As for the heel of your hand question, it probably counts as anchoring, I just gave it a go on my guitar and found it rotated my shoulder/wrist backwards a bit so probably not the most efficient way to rest your hand imo. Check this thread if you're worried/want more info:

My hand is very relaxed when I do just about everything. When I do practice sweeping, I tend to be a little less loose to get a more percussive sound, rather than soung like a chord.

Also, when I do very fast picking and tremelos, I do tend to use my elbow a lot more than my wrist. Is that ok or a mistake?
My knowledge of sweep picking isn't great, but I'm thinking you should be muting to stop the notes bleeding into each other rather than picking harder/tensing up - anyone with more sweeping experience want to weigh in??

Generally you should be using your wrist for small motions (single string work) and your elbow for larger motions (changing from string to string). A lot of people anchor to 'help' with their tremolo picking, they just tense their whole arm and go nuts - it's more efficient to unanchor and just get a good alternate picking technique up
Before I say anything, I want to be clear that the tone here is in no way defensive. Sometime I come across that way, and I don't want to mistakenly offend someone.

I don't anchor my hand down per se; I read the Freepower sticky and I don't think that's what I do. Maybe my explanation was unclear (having reread it, it does seem a bit vague).

What I normally do is have my hand floating for the bottom four strings with my index finger on my left hand muting unwanted strings. When I play higher passagers, I normally will either mute the strings with my index finger or palm mute to remove any unwanted sound. I don't find it uncomforatble to play with my hand against the strings or floating.

When I tremelo, I don't really tense and go nuts. I have a very controlled tremelo, it's just coming more from my elbow then from my wrist (my elbow is pretty loose and normally rests on the guitar when I'm not playing a faster passage. In that case, it is normally free and loose).

As for my sweeps, I don't really lock my wrist, but as you yourself said, it is generally better to use my elbow for larger motions, as a sweep would require.
I usually rest my hand near the bridge when playing the B and high E strings. However, I have noticed it is more difficult to pick at high speed doing this, so I have begun to lift my hand about a centimeter to avoid friction between the strings I'm trying to mute and my hand.

And thanks for the video. That reassured me a great deal.