I Can Feel the Inside Egde of a New Crown. Will This Let Bacteria in and Cause Tooth Decay?

The transition from your dental crown to your tooth should be smooth and not have a "gap." A space between the two could lead to bacterial migration under your crown and ultimately to decay. I would call your dentist and have them evaluate the fit. I'm sure they will replace it if necessary. Good luck.

This depends on if what you are feeling is an open margin (which is a gap between the tooth and the crown) or overhang (which is they made the crown a little too thick and it hangs over the edge of the tooth a little).  If it is an open margin then bacteria can get in.  If it is overhang, then it may still be sealed and free from bacteria.  either way, I'd go back to the dentist and get it checked out.

You should not be able to feel the edge of your new crown. I would call your doctor to make an appointment to have that corrected.