Q1 - By the time we ____, everyone had left.
had arrived Why can't you use both here?
Q2 - I _____ a long time ago.
Either could be used here. Why can you use both here?
Q3 - By that time, everybody ____ exhausted.
Either could be used here. This one I kind of get.
Q4 - She told me she ____ it ages ago.
Either could be used here. Please someone clarify this one as well
I would say:
1 The people clearly left first- before your arrival.
2 There's nothing in the context to restrict the meaning to one.
3 There classic rules of indirect speech would recommend backshifting to the past perfect, but in everyday usage, we often don't bother.