Hi Tobias,
I will try to answer your questions one by one:
Yes, in this case the laser is applied along x-y plane keeping z constant. If the surface is tilted along z, you then have to take in to consideration the z plane also to have a consistent laser heat distribution. I have performed that case also, have a look here:
Yes, you are right, the laser heat source is moving only. Whereas, the heat flux remains constant.
I am not sure here, though the formulation is taken from a research paper here: Finite element simulation of laser transmission welding of dissimilar materials between polyvinylidene fluoride and titanium
This is a typical Gaussian power distribution formula.
Yes, FEM solver
In order to capture the laser motion properly. Using a coarser time step can lead to odd temperature and heat flux distributions. So two very important things here is the much finer mesh on the laser impacting surface + finer time stepping.
Hope this helps.
Best,
Ahmed