Nice posts Genitric.

Good thread also. I think all 4 hands could have their own thread and I really wish we would more often go into these details when analyzing hands.

Here are my thoughts and questions.

Hand1
My kicker usually plays a part as well. To me it matters wether I have A7 or 72, because when we have MPTP there are a lot more worse hands that call. That's also the reason I bet, together that I don't mind taking it down right here because lots of turn cards could be bad for us.
3/4 PSB is what I would do, but I would like to here thoughts about other betsizes.
Q: Why not PSB? Does the flush draw being out there changes anything?

Hand 2
I raise here, because villain likely folds 65-75%. If he calls, on a lot of flops he likely folds, I think 65-75% as well. Don't c-bet some flops and you're overall EV goes up even more.
If you just call, SB is likely to come along as is BB. It's much harder to win the hand without flopping good.
Sauce's respond is very I good, I wish he would go into follow ups on next streets a lot more!

Hand 3
I probably call because I expect to win a lot when I hit against this opponent. In general if villain is a little tighter I like 3-betting more.

It also depends on the gap between his CO raising range and 3-betting calling range.
If it's wide enough we have lots of fold equity, and can 3-bet lots of hands profitably because of it.
If it's not very wide, the 3-bet itself isn't very profitable and we have to look at winning flops:
- If villain calls the 3-bet light, we can 3-bet less good hands for value (AQ, AJ, KQ maybe)
- if villain doesn't call light, he basically has a strong hand (little FE, small 3-bet calling range) means we can fold preflop or 3-bet hands like small PP's, maybe SC's to flop a monster and get allin. Or call and c/f missed flops.

Calling preflop intended to c/r lots of flops is an interesting line. If villain isn't spewy postflop this can work as a bluff, because he has to have a good hand. His raising range has to be wide and his flop calling range has to be small, which he likely is.
A flop c/r is something like 2-1 and a preflop 3-bet is 3-1 followed by a 3/4-1 on the flop.
I don't know if my reasoning is anything but solid, but let's take an example:
1) Let's say pre we 3-bet 15 to win 5. When called on the flop we bet 20 in a 30 pot. In all, it cost 35.
Ofcourse we take it down preflop a decent amount of times. We only win like 5 BB's then though.
But when we take it down on the flop we win 30 which is great.

2) When we call pre for 4 and c/r a flop bet of 7 to 25 it costs 29.
We never win anything preflop. We win often on the flop, but we only win 16BB each time.

I think to take this one step further we have to assign percentages of how often we win preflop and on the flop which each play. I don't know if it's possible, it would be great to try.

Hand 4
I have nothing to add to the great input that has already been given.
Genetric, if you (or we in general) could back up your reasoning with some calculations it would be awesome.