Thanks for the replies guys.
1. I guess what I mean by "better" is a tank that is more rounded or able to handle most situations.
Arbitrary. There are so many variables that can go into a mission- the mission goals, your starting situation, for example, supply, ammunition, support. That might determine more than what your chances are than what you think is the 'best' tank, aside from the user's individual skill.
If not that, then the tank with the biggest, most bad-ass gun.

I know everyone has their weak spot, but some weaknesses are "weaker" than others, if you get what I mean

Again, that really isn't the mark of success here. The T-72 and T-80 models have the largest bore diameters and can often fire ammunition types not available to Western tanks, i.e., a gun launched anti-tank missile or a large HE fragmentation round. If you just expect to succeed on that alone, you might be overlooking mobility as a factor, which is very important. If you sit there with the knowledge you have the biggest gun, you have a false sense of security. You might just find that a tank just suits you better because of its intereface, or its placement of optics, its over all layout.
You might as well consider another subjective standard of what is better to you- that is to say, which tanks you simply enjoy more. That's an easier way to measure
better than I think what you are intending here. For instance, I really enjoy the older tanks that don't have thermal imaging, the problem is that as consequence of that, they can suffer an artificial drawback of lower frame rates in more detailed scenes, since the TIS views draw less detail when you scan with them. I still consider them challenging and fun, though.
I prefer the amount of ammunition the M1A1 carries- lots of machine gun ammmo, which is important. I prefer what's often considered an inferior fire control system with respect to automatic lead added to moving targets, it feels more natural to me. I prefer the fact that the gun isn't raised between loading cycles, you can switch to coax between shots. The T-72 or other tanks that do that can really get creamed in that respect. As you're taking out vehicles, enemy troops can start popping up and shoot, and you're vulnerable during the period the machine gun can't be used while the next round is rammed into the gun. Finally, the .50 cal gives you one more option the Leopards or the CR2 don't have.
None of these will probably determine success over just an experienced player's skill and available support; you'll learn to anticipate these quirks with practice and experience and make up the difference with better tactics. The differences are going to be more subtle for tanks of the same generation. You're generally well protected up front, you have a lethal gun, ammunition types are really the difference there. Mobility is another thing to consider.
4. No one-hit kills here? Assuming good shots, how many hits usually? Just a ballpark figure would be great... somehow I feel like putting 6 rounds into an enemy tank is just taking too long.
Sure there are- happens plenty of times. There's no way to determine how many hits. You might shoot all day at the front of a T-80U, if it can't get through, it can't get through. The type of ammunition, placement of the shot and what it hits is what counts, plus I understand some random modifiers added into the calculation just to account for the randomness of real life.
I just finished the M1A1 tutorial. While I had a rockin'-good time with the gunnery tutorial, I must admit that the rest of it made little sense. I could understand what it said, but I did not feel as if I applied myself correctly. For instance, why even bother with the gunnery position when you can be a TC and your gunner does a better job than you?
A matter of taste, depends on the sitution. Sometimes the computer can detect something faster than I can, sometimes it doesn't seem to pick up something that I think it should have. Sometimes it hits when I can't, sometimes the reverse is true.
And can formation and spacing commands only be issued on the map screen?
No.
I was once in a situation wherein I was behind a crest of a hill with the enemy on the other side. Hitting the "E" button for a hull-down position did nothing, and I lost my TC and stabilization system in the process.
There's no way to know what happened here based on this description. Your tank might have already been in a position the computer driver thinks is hull down- you even said you were behind the crest of a hill, so I don't know what you expected here or what the situation was.
1) Hull down is highly relative. What's hull down with respect to one enemy on site might not be to many others. The computer can't read your mind and know which one is specifically the one meant, but generally it will follow rules of thumb to find hull down positions and does a reasonable job.
2) Hull down is not turret down or in complete defile. You can still be hit, A TC can still be exposed.