I'm going to make a couple of assumptions first:
1 - you don't have a VCDS so there are no codes you can pull to assist with the diagnosis
2 - you have not actually tested the battery in the car
Based upon what you described, the fact that it fires up and drives as per normal after a jump start would lend me to believe the issue is with the battery itself. Even relatively new batteries have been known to fail (i.e bad cell) and therefore, I'd recommend you test the battery to ensure it holds a full charge. If the battery is not charging at all then the issue could be the alternator...however, let's troubleshoot one issue at a time.
As for the 'sparks', I've got no idea what they could be and may be a red herring or something major; related or not.