can LAMMPS do this?

Hello Dr. Francesco.

(ii) can be done by post processing a dump using computes. For example for (2) you could use compute group group command to calculate the potential energy between two atoms at every time step.
I am not sure about about one but I think it could be done may using read dump in a loop.

Also I have a post processing code that takes in custom lammps trajectories that strips the atom data in every frame. I will make it as an open source soon.
I will send them to you offline if you would like for now.