Can a prosecuting attorney know an accuser and some of the jurors on a case over that they are prosecuting?

The accuser knowing the prosecutor is irrelevant: they are on the same "side" so there is no conflict and no impairment of fairness.
The prosecutor or accuser knowing jurors personally, however, could lead to bias: juries are supposed to have no connection to any of the participants, so that their decision is based solely on the facts of the case. If the prosecutor or the accuser knows jurors, that *could* represent a denial of due process (that is, of judicial fairness) and grounds to appeal an adverse verdict (though the complaint about the situation should be raised promptly "on the record" with the judge before trial or at most as trial starts: sometimes appellage courts will not hear appeals unless the objection or issue was raised at trial in a timely manner).
Whether thereis actually bias depends on the strength and nature of the connection. For example, just having gone to school with somone is almost certainly not enough: we have all gone to school with people whom we may recognize, but have no relationship with, and where knowing them "at a distance" does not impact our judgment or fairness. But having been teammates on a school sport, been in the same club, having been friends, etc. could show a close-enough relationship as to cause, or at least strongly suggest, impermissible bias.