Is it possible to get a hat that won’t mess up the awesome mohawk

You cannot change factions in TOR — what you pick is what you get.

That said, there are small differences depending on whether you are Light Side / Dark Side, such as verbal cosmetic changes in conversation. And your choices may affect companion affection.

Flashpoints are repeatable and have up to +/- 250 points' worth of dark/light decisions among them, and Diplomacy crew missions can yield DSP/LSP as well, so you can always completely reverse your stance (although that could potentially take a /lot/ of work...).

I've found one case where an ability is different between the mirrors, but even beyond that there are definitely some differences between how the mirrored abilities themselves play out. The differences mainly seem to be in the animations used (and the speed differences therein) as well as travel time from projectile to target. As such, most of these differences have very little effect except in PVP, where a few seconds can be critical.

Just for the sake of context, here are the mirrors:

  - Jedi Knight      <-> Sith Warrior
  - Jedi Consular    <-> Sith Inquisitor
  - Republic Trooper <-> Bounty Hunter
  - Smuggler         <-> Imperial Agent

Obviously maintaining a list of every single difference would be unwieldy not to mention probably end up outdated, but here are some differences I've found to illustrate my point:

• Bounty Hunter's "Unload" doesn't get interrupted if you take damage, but the Trooper's Full Auto does. This makes the Bounty Hunter's ability better.

• The Bounty Hunter's Death From Above starts applying its damage immediately, compared to the Trooper's Mortar Volley which takes a few seconds before damage starts being applied.

• The Sith Inquisitor's Shock does its damage immediately, whereas the Jedi Consular's Project ability has a longer animation and a travel time.

• Smuggler's Dirty Kick stops the forward movement of the smuggler, where as the Imperial Agent's version does not stop the forward movement of the agent.

• The Imperial Agent's Flash Bang is on a 60 second cooldown, but the Smuggler's Flash Grenade is on a 90 second cooldown. They otherwise appear to be identical. They plan to patch it soon.

• The Imperial Agent's Backstab happens instantly. The Smuggler's Back Blast animation takes longer.

• The Imperial Agent's Explosive Probe animation is quick and damage happens almost instantly, whereas the Smuggler's Sabotage Charge has a longer animation plus the damage isn't applied until the charge travels to the target.

• I see at least one example of ability difference (assuming TorHead can be trusted). The Consular gets a level 46 ability, Unity, which lets them and their companion reduce damage by 50% for 15 seconds. The Inquisitor has a level 46 ability called Sacrifice which nearly kills their companion, but heals themselves 40%. Pretty different effects. This is biggest difference I've seen, and haven't heard of any others like this.

So to answer your question directly, no, they aren't perfectly mirrored. I think the animation speeds have a much larger impact on how the mirrored classes play differently, as opposed to the minor round-off problem in the conversion such as that between heat and ammo. But even then, the mirroring is close enough that it probably won't matter to anyone except in PVP.