Hoo boy, lets see if I can answer some of those:
1. Yep, correct.
2. There is the Alpha Strike Companion which has advanced rules, as well as the Combat Manual series that has been coming out, which contains more info about specific factions and forces in that faction. These are available in PDF format and hard copy from BattleCorp, DriveThruRpg, and a couple other major book sellers.
3. First, I never play this way. I always start units within 2" of the 'home' edge of the map, or set up around an objective if it is more a defense/ambush type game. However, you are reading it correctly. Technically, there are no units on the map when the game begins. When a unit takes its first move, you just pick a point along your home edge, and measure from there.
4./5. It's different, but not really an huge issue. It does make it easier to avoid 'wasting' damage since you don't have to declare all your targets first, but since the looser goes first, they have to worry about whether their opponent has any HT weapons that could mess with them if they choose to overheat, and the player that goes second knows which of his units will be gone anyway, and can safely choose to overheat them on their last shot without any real consequence. Mainly, it's just a whole lot faster to resolve and track without all the target declaration.
6. I think it is in the errata (there are errata posted on this forum) but it is very slightly different now. A unit that moves more than 1" gets it's full TMM. A unit that moves less than 1" is standing still and gets a 0 TMM. Standing still also makes the units own to-hit rolls easier by one point, so it is still worth doing. It no longer really matters how far you move, just that you moved at all.
7. Usually, heat. Heat subtracts a flat 2" from movement for each point on the scale. So, if you start at 8" of move, take two motive crits, and overheat for one point, you will be at 0" move.
8. Standard Alpha Strike just has woods...just the one type. On p.69 of the rulebook though, you can find the rules for light, heavy, and ultra-heavy woods. They are 'advanced' terrain. Also, there is an important errata on woods. They now take effect if either the attacker or the target occupy woods, not just the target. Basically, no shooting out of the edge of the woods for free.
9. Yep.
10. Correct.
11./12. roll for the crit in both cases. All that language about 'doesn't count as an attack' is just so that no one mis-reads and tries to say, "Ha! Your Atlas did one point of damage to me as a result of the charge! That was its attack for the turn! Fear my rules lawyering skills!!!" The damage from a charge is a separate hit, and if it causes structure damage gets its own crit roll.
13. Yep. 2" or more of Water = -1 heat in the end phase.
14. Correct.
15. Correct. You have to go underwater to have it cool your mech down.
16. In hex-map play, adjacent hexes are considered base-to-base contact, and the mechs would have to punch each other (or another mech they were in base-to-base contact with) and could not make a ranged attack. For the MEL special, I believe an attacker with that special could choose to make a physical attack from one hex away. The attacker could also choose to make a ranged attack instead. Neither the attacker or defender would be considered in base-to-base contact. MEL just gives you the option to make physical attacks from farther away in this case, it doesn't force you to.
17. Not at all safe to say. Plenty of mechs have different walk/jump ranges. The Shadow Hawk, the Mist Lynx, the Anvil, the Jenner. All have less jump move than walk. There are also units (usually with improved jump jets or partial wings) that have MORE jump move than walk.
18. Hey, whatever works for you!
19. 0* is minimal damage (p.38) and it can come on more than just IF specials. What it means is, if your to-hit roll succeeds, roll another D6: 1-3, you didn't do any damage. 4-6 you did one point of damage (or 2 if it was a shot in the rear).