Talking about the FPS games

Who doesn’t like FPS games, they can be fun to play and enjoyable to experience, especially nowadays when there is VR.
But what I want to talk about is something very deep, and for it, I have many questions.

So while I was playing CS 1.6/GO I noticed that for example the colour of my arms in FP camera didn’t match with my character in TP camera, same while I was playing Valorant, there was always something off about it, and it looked too perfect for the full-body character to have FP camera. That is what I thought of course, in the beginning, when I started playing these games. But lately, I started playing GTA V and noticed this weird FP camera with full-body mesh. I, at that moment, figured out that CS and Valorant don’t use full-body mesh with FP camera but only rigged arms in FP. This is very weird for me because my whole life I thought that they use full-body mesh with FP camera(I think?).
Yet recently I played the game named The Cycle, in which it has CS/Valorant like experience but with something extra. When I look down, I now see my body and feet; the same damn experience like CS/Val but with full-body.
I want to make a game similar to CS/Valorant but in a way like it is made in The Cycle(the game being Co-op, single-player experience).
So I have a few questions now about it.

How do I animate my full-body character to look clean in the FP camera and when I look at the enemy? (I don’t want to make 2x of same different animations just for FP and TP character(enemy)
Where do I put my camera to look in the same or similar way as it does in those games that I mentioned?
Do I need a camera boom?