Why has there been no moon for 2 nights straight
The Moon is out of sight for a few nights every four weeks, more or less. It moves around the sky slowly. Sometimes it's far from the Sun (as seen from our planet), and that's when you see it at night, up in the sky. Other times it seems close to the Sun, and then of course you won't see it at night. Then the cycle repeats, over and over again. Takes a bit over 4 weeks to repeat.

The star-like things moving in the sky can be many things. Usually they are satellites in orbit around Earth, or airplanes flying at high altitude.