I'm jumping in a bit late in the discussion again, but I thought I'd clear up a couple things I said before.
By mouth position, I was mostly referring to your embouchure. Making sure that your lips are properly placed, that kind of thing.
As for warming up...I would suggest just working through scales for now. Go slowly through 5-6 of them, say a quarter note or so per pitch. You can also mess around with different rhythms and such.
Another useful warmup exercise with scales deals with "Intervals."
Play the 1st note of the scale, then the 2nd, then the 1st, then the third, then the 1st, then the 4th, then the 1st, and so on. Go up and down the scale.
Doing both of those exercises for a few scales before doing serious playing warms up the instrument and mouthpiece, and gets your lips ready for the assault of playing real music. After warmup, then you can tune your sax and the pitch will stick better, since the horn is the same temperature. A cold horn will typically blow flat until it warms up.
The above warmups are very basic ones, and there are hundred of other things you could mix in with them. Some of the exercises on Pete's site make great warmups.
5-12 hours a day is a lot for a beginner, and it is certainly possible that your lips have tired out some. However, if you do take steady breaks, you will be able to play for a fair amount of time. For me, I play an hour in band early in the morning. After school I come home and play for another hour. I grab a quick bite to eat and then rush off to rehearsal, where I'll play for 4+ hours. At rehearsal, if we are just running over everything without any breaks, I'll be exhausted by the end of it. If I have even 5 minutes here and there, I'm totally fine.
With reed strengths... Some players make a lot of squeaking noises if their reed is: 1. Bad, 2. Too Dry, 3. Too Wet 4. Too Hard, or 5. Too soft. Since you tried different reeds of the same variety, I felt it safe to assume that 1-3 weren't an issue. That leaves too hard or too soft. Although it is common to start players on #2 reeds (I had no idea that anything lighter even existed until I read a post above), many school start their students on 2.5s also. The overall difference between 2 and 2.5 isn't very much, and if things improved, could tell you that all that was needed was a harder reed. With the amount that you are playing, I think this is probably a good step-up anyways. Still, if 2.5 doesn't feel right after a certain amount of playing with it, then don't. A lot of people move to harder reeds too quickly.
As for testing out the reeds you bought...just get yourself warmed up. Make sure they are all moist and then play a few scales and then some music on them. See what feels right. The 3 and 3.5s might be a bit hard for you though. At the same time, without hearing you play, I have no idea. It all depends on the musician him/herself. You will get a deeper sound on the harder reeds, but you will lose the controllability of the lighter ones. It is certainly possible to get the same quality of sound on a lighter reed, with enough practice.
Another thing...reed strengths vary between brands (ie. a 3 Rico is different than a 3 Vandoren Java, which is still even different from a Vandoren V16). If you google for "Saxophone Reed Strength Chart" I'm sure you'd be able to find the exact comparisons.
And don't worry too much about the "permanent damage" thing from the Teal book. Don't get me wrong, the book is an excellent resource, but it is a bit...different, for some things. It even goes so far as to say that those with overbites should never play the saxophone, yet when I started I had one, and am still darn good for my age. Unless you are working on the extreme ranges of the horn, and pushing the boundaries you won't cause nerve damage. And most of those boundaries you have a couple years before you'll reach.
If you are already picking up scales and getting a few tunes down, you definitely have some skills! Don't put yourself down too much. As jazz great Stan Getz said on his 50th birthday "I think I'm finally learning how to play the saxophone!" (or something along those lines).