What it means is that you will be a Rogue 12 / Assassin 8 and then take your shadowdancer level at the 21st level.

This is due to the way your base attack bonus progression is rounded. If you take your level of Shadowdancer at level 20 or before you will get your attack bonus rounded down, whereas if you take it after level 20 it will not affect you. For HotU, I wouldn't worry too much about weapon availability. You can craft your own weapons with the help of the blacksmith starting in act 2.

The handaxe's x3 critical threat is about equivalent to the Short Sword's 19-20/x2 threat. Take your preference; I prefer bigger range to bigger multipliers personally.

lolGameBanshee...

If you have weapon focus: hand axe then there's a guaranteed drop of Offhand Axe +3 (1d6 sonic, Bonus Feat: Two-weapon fighting) on Olgin boss and in Three Guardian chest (both Undermountain One).

Since the mods on Ice Reaver aren't stand-out, you'll probably just end up upgrading through Rizolvir. Some weapons may have mods you want to keep even "sacrificing" a Rivolvir enchanment, but hand axe isn't really one of them.

As Darvin said, Handaxe and Short Sword are basically identical. One crits for more but less often (Handaxe) and the other crits more often but for less damage (Short Sword).

Those two and Mace are the main rogue weapons (Mace since, by default, a lot more stuff is immune to Slashing/Piercing than Bludgeoning and Sneak Attack damage can't crit).

Indeed. In HotU you can definitely make a good weapon of any type.