I'm experimenting with a Barb 4 / Fighter X build. I will take the grappling feat (I know the grappling feat is controversial, but I feel like there might be creative ways to use it). I will take unarmed fighting style, and bear totem. I was wondering if someone could clarify the damage output.

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Analysis: Let's say I have 3 attacks per action (Fighter 11). I grapple with my first attack and succeed. Then I attack with my free hand, with advantage. From what I understand, I get 1d8 STR. Then I can make one more attack with 1d8, with advantage. Then, next turn, the grapple is still held. I deal 1d4 bludgeoning damage for free (twisting the enemies arm or something?). Then I get three attacks, each (1d8 STR), with advantage. If I want to do something like a shove or a pin, that counts as one of the three attacks.

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The descriptions are a bit confusing on dnd beyond:

Unarmed fighting:

Your unarmed strikes can deal bludgeoning damage equal to 1d6 5 on a hit. If you aren’t wielding any weapons or a shield when you make the attack roll, the d6 becomes a d8.

So my character isn't wielding weapons or a shield... so does that make the attack a d8? Or since I only have one free hand it's a d6? As written, it seems like a d8.

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Fighting Style: Unarmed Fighting (grapple) (Special)

At the start of each of your turns, you can deal 1d4 bludgeoning damage to one creature grappled by you.

Is this a bonus action? Do I only get to apply it once per turn or every attack?

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I believe my analysis above is correct, but reading through some of the forums there has been a lot of conflicting information.

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Lastly, with Barb rage, fists count as a strength weapon yes? So I would actually get 2 on top of that while raging?