Basic PTM - Critical Path Assignment

I have a question regarding the critical path analysis and the scheduling. On the critical path analysis, do we need to differentiate which department is doing the work (since there are a few hand-offs) or should all of the tasks be put into a single pool and the predecessors be determined blind of what department is doing it? Or is this irrelevant because the entire crew is ourselves and a buddy?

What do you need to do critical path? Label, Time to complete, Immediate Predecessor.

For the critical path assignment, should we assume we only have two people or is that only for the calendar?

What do you need to do critical path? Label, Time to complete, Immediate Predecessor.