Is there a way to detect the current camera mode?
The camera's mode can be forced with Game.ForceFirstPerson () and Game.ForceThirdPerson ().
But there doesn't seem to be a way to detect what the camera is currently set at.

You can use IsPC1stPerson, it returns 1 if the player's in 1st person, and 0 otherwise.

Cool! Thanks Poulpe_38!

Edit:

That's not in the Scripting Reference for some reason - Maybe because it's a Console Command.
Hopefully Console Commands work in Papyrus scripts.

Next question: Is there a way to get the distance of the camera from the player's 3rd-person view?
And Is there's a way to set that distance?

Unfortunately not.

It's a little ugly, but maybe you can use http://www.creationkit.com/MoveToNode_-_ObjectReference to put an object at the camera node. (Is that still a node?)

I just saw that, it was present in GECK (fallout editor), but got removed apparently.

I'm not sur if there is a way now to detect the Player's PoV via Papyrus scripts, unfortunately.

You can query an animation variable:

Game.GetPlayer().GetAnimationVariableInt("i1stPerson") as bool

Use it in conditionals or assign to a bool variable.