Hey there! Welcome to the boards! Here's some XP!
One of the things that it took me a while to realize is that my concept did not always have to be represented by the mechanics, but that I could rather "reskin" the mechanics to look the way I wanted.
As a relevant example for you, it seems you want to do some two weapon fighting but you want to use your fists. And it sounds like you want to do this by the rules. But obviously, it's no fun fighting with fist that deal 1 + Str/Dex damage (or in your case 1d4 + Str/Dex damage since you have Tavern Brawler).
So, first question is... do you have the Dual Wielder feat? If so, use two rapiers. If not, use two shortswords.
Now hear me out, because I know you're probably thinking, "Why would I do that? I want to use my FISTS!
And yes, you can still do this. Because let me ask you... what makes a shortsword a shortsword? Or a rapier a rapier? Because see, I can take a weapon that deals 1d6 damage, has the light and finesse properties, and reimagine it as a gauntlet. Or a punch dagger. Or brass knuckles. There is nothing saying that a weapon that deals 1d6 damage with the light and finesse property HAS to be a shortsword. We have just all agreed that these mechanics should be shaped into a shortsword. But you can reimagine it anyway you want.
So I would suggest talking to your DM about:
1) requesting to retrain the Tavern Brawler feat into something else (unless you really want it for more than the 1d4 unarmed strike damage). The stat bump or Dual Wielder feat would be better.
2) Requesting to reskin shortswords or rapiers into brass knuckles (or something similar). As long as you have proficiency with the weapon and don't change the mechanics, its effectively the same thing. If is also easy to request for the weapon to deal bludgeoning damage rather than slashing or piercing, since each of those damage types are equal to one another. The only difference is what is thematically appropriate for the weapon.
This would give you an effective finesse weapon to use with your sneak attacks, give you the thematic image of using your fist to deal the damage, and remain very close to the rules.
I would say an unarmed strike can count for two weapon fighting, but not for the Dual Wielder feat since it specifically states you need to wield two weapons.
Edit: Nope. While silly, the Two Weapon Fighting specifies the off-hand attack must be a light melee weapon, which unarmed strike does not count for.
You would only get three attacks if you have the Extra Attack feature (such as being a level 5 fighter) and you use your attack action and a bonus action to get all three attacks.
No. You can only give away an attack from your main attack action, since Commander's Strike also requires a bonus action to give the attack to an ally. Since you need the bonus action for the maneuver, you couldn't also take the bonus action for an attack.
Yes, you can only make one sneak attack a round, unless you go with the Scout (a rogue archetype that allows for a second sneak attack in a round).