Hello,
I will attempt to give you some answers but it has been a long time...

At 12th level, how does Charisma effect the length of the Charm spell?
Charisma has an impact on all your Charm/Mezz line of spells so if you plan on using this strategy then the higher the better.

Is this effected by Tashan at all?
Tashan lowers the resist on the mob so it will help to get your spell to 'take'.

From 8th to 11th how well does this strategy work out on evens/yellows?
1) Tashan
2) Color Flux (after pet engages)
3) Root or Blind / Fear

You should always open with a Tash of some sort,
the color series are your stuns and is good to cast when you are tanking for your pet. If you root the mob your pet is going to take a beating and then you will have to jump in and tank for pet or it will die, If pet is already dead I would suggest rooting. Blind will not stop it from attacking you in my experience and fear is only good to use when the mob is snared in some way or you are trying to get away. If you are pretty sure that there aren't and mobs in the area to be aggro'd then Fear is ok to cast otherwise you will have company when it returns.

From 12th on how well does this strategy work out on evens/yellows?
(Using highest level pet possible per level, fully buffed)
1) Open with Tashan
Should always open with a Tash.
2) After Pet engages cast "Whirl-Til"
Whirl is a stun, Once pet hits or you land a DD WTYH will break.
3) Cast Choke (optional)
Breaks WTYH.
4) Med til pet starts getting hit, cast "Whirl" again
Pet WILL be getting hit from the get go.
5) Repeat 4 til mob dies
Pet will be getting low so you will probably be tanking at this point unless you let pet die.

This looks good on paper, but would it work in the game? Recast time on "Whirl" a factor here?
Yes, Whirl has a pretty long recast time but you can alternate with a color series or dd here.
As you get higher in level you will want to use Charm OVER having a pet, this will allow you to take out TWO or more mobs with less mana. Remember to refresh your charm if you have an extended battle. When you have a sufficiently 'beat on' pet just do /pet guard here and move away a distance so when he breaks you have time to root then hopefully finish off with a DD or two.

At 44th lvl and on you will see a significant improvement in your pets. The 49th pet is just amazing, buffed up with SLTW and 2 daggers it quad hits for 52's at an amazing speed.

What good are the vials created via Thicken Mana? Are they stackable if you use stackable vials? Can you use them in combat?

Haven't found them useful for anything outside of tailoring Wu's fighting gauntlets.

Has anyone figured out how to use the Gem Cutter? What benefit does this actually have on Jewel Crafting?

Some have said that the gem cutter did have an impact on jewelcraft but that was only in beta.

Hope this helps in some way.

Zealott Enrapture
51 lvl Illusionist