Is it alright to keep conversations on with two partners of a fund (got in touch with them from two different introductions) at the same time?

One of the first questions you should ask your target is about the decision-making.  Are the partners in a collaborative environment, or do they each have their own bucket of resources which they themselves direct.  If it’s the former, chances are good you got dual introductions because of overzealous assistants or automation.  In this case, there’s no point in having a dual track, so you might as well fess up and ask if you should be talking to one or the other.  If it’s the latter, then you should probably identify anyway so as to ensure that both of you are talking to the right people.