Subject: 1)More common, lunar or solar eclipse? 2)Why elliptical orbits?

I am a physics teacher and I have done a fair amount of coursework in astronomy, 
but there are two questions I've gotten recently (from the same student, of course) 
that I can't adequately answer.  
1) Are lunar eclipses more frequent than solar eclipses (and if so why)?  Obviously 
lunar eclipses can be seen from anywhere on the night side while solar eclipses 
are seen from only a small part of the sunlit side of the earth, but if we are talking 
about basic frequency, is one more common?(my common sense said lunar, 
because the earth has a bigger shadow than the moon, but my student countered 
with the idea that this should be balanced out by the earth being a proportionally 
larger object to be hit with the moon's shadow)  What's the deal?

2) We have been studying Kepler's laws of planetary motion, and when talking 
about how all closed orbits are ellipses, I got this question: why are they all 
ellipses?  Other than "that's the way they started out" (because there are initial 
velocities of orbiting bodies that could result in circular orbits) is there an answer 
to this one? 

Thanks so much

Re: 1)More common, lunar or solar eclipse? 2)Why elliptical orbits?