I'll share some of my thoughts, but (disclaimer) some of your questions constitute requests for engineering advice, which we are discouraged from providing. We can advise you on the appropriate program usage to mimic boundary conditions and applied loads that are, in your engineering judgement, applicable, but not on what assumptions to make (that's an engineering call, not a software one).
So... rivets and the skin in their immediate vicinity can fatigue. You of course want your modeling assumptions to represent the structural response with high fidelity, because these failures can be consequential:
Additional perspective... I witnessed (periferally) the development of a protoype capacitive sensor at the manufacturing systems technology lab at the University of Washington in Seattle (Prof Joe Garbini). A Boeing funded (of course) effort, it was used to quantify various aspects of geometric imperfections in the pre-drilled holes in aircraft skin that accept rivets. So, at least at the time, small imperfections in the rivet hole geometry were considered to be a possible contributing factor in fatigue failure.
We don't know the geometry of the portion of aircraft structure you are including in your model, and we certainly don't know that of the structure that extends beyond the boundaries of your model. But based on what I imagine it to look like, I offer you the following:
1 It is probably best, initially, to use force distributed (not rigid) remote points at the boundaries of your model. Actually, you might conduct an investigation... use a few different models truncated at different locations, and by trial and error determine what BCs on the cut boundaries of your smallest model most closely predict the stresses at the same locations in a larger one. This might help you establish most appropriate boundary conditions. Or you might consider submodeling:
2. See my answer to (1) above. Also, you might consider trying a couple of features that are not natively exposed in Mechanical (and so would require the use of command objects to implement). These are (a) PML ("perfectly matched layers"):
and (b) the structural infinite boundary element (INFIN257):
The Help articles in the images above are in the Mechanical APDL Help. PML is probably easier to implement.
3. Probably best to use frictional contact anywhere there is contact between any of the rivet surfaces and those hole/skin surfaces that they contact. You might consider creating a localized detailed model of an individual rivet and the drilled material through which it passes. My guess is that the rivets are installed via some swaging process that causes plastic deformation, modest geometry changes, and might "press fit" the rivet shank against the hole through which it passes... a prestressed state that might be an important starting point for subsequent application of other external loads.
4. I was under the impression that the most deleterious loads are those associated with landing. I've heard (this is unsubstantiated) that, looking down the length of fuselages of commercial aircraft that have been in service for some time, one can easily see that these structures are no longer straight - permanent bends are brow-raisingly apparent. I remember hearing that this is a consequence of forces the structure is subjected to when landing. Ever experienced a hard landing? So my guess is that the external loads reaching a modeled portion of the aicraft structure can probably be treaded as quasi-static... applied (maybe) as nonzero remote displacements at the boundaries of your model. The response of the entire aircraft however is almost sure to be dynamic - landing forces probably encourage some natural frequencies to participate in the response. Submodeling again comes to mind...
Best wishes and have a safe flight.