Can I tap a creature with summoning sickness to pay "tap an untapped creature you control" costs?
Yes, you can. Relevant rule:


  302.6. A creature’s activated ability with the tap symbol or the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since his or her most recent turn began. A creature can’t attack unless it has been under its controller’s control continuously since his or her most recent turn began. This rule is informally called the “summoning sickness” rule.


This is the tap symbol:



The only limit that summoning sickness imposes is about the tap symbol . "Tap an untapped Vampire you control" is not the tap symbol.

It has nothing to do with being from another source. Heritage Druid could tap herself the turn she comes out.