newtonian mechanics - What does the Moon's orbit around the Sun look like?

I'm curious as to what the Moon's orbit around the Sun looks like. If there's an answer, what's the intuition for it? Here are some things I'm assuming when trying to tackle this question:

1. 
   

   The Moon's orbit must be concave toward the Sun.

   
   


2. 
   

   The Moon speeds up as it goes toward the Sun, and it slows down as it moves away.

   
   


3. 
   

   For an observer on the Earth, the Moon appears to orbit the Earth roughly $13$ times a year.

   
   
   


4. 
   

   The Earth, the Moon, and the Sun remain in the same plane.