First make sure there is weather stripping between the skylight frame and the curb, assuming this is a curb mount. sometimes there is not a seal inserted at that joint. If that is not an issue, then you could certainly install a frame around the well at the ceiling level and insert a piece of clear acrylic to keep cold from dropping into the room. I have done this at a previous residence with great success. Good luck

Without knowing the specifics of the skylight brand and condition, we would not be able to answer the question with confidence.

We use Velux skylights. During re-roofs, we typically find most skylights are not in good condition and/or were not installed properly. 

It is difficult to suggest an exact temperature for shingle installation. There are several factors involved such as your geographical location, the amount of sun exposure at your particular home, etc. As always, we would suggest referring to your shingle manufacturer's guidelines.

There is a bee spray you can mix in a pump up and reach the higher carpenter bee holes. This worked for me.

Michael,

Eric pretty much nailed it. 

It is not usually worth it in my opinion and especially given the nature of most leaks and the condition of most sheathing. 

Roofs aren't cheap so I think the math usually plays out that the full tear off is a better idea based on the fact that you get a better install and will likely have a roof that will last longer.

WoW Home Solutions

I have seen a lot of great DIY carpenter bee traps that fill up with bees. I have friends that say the traps keep them out of the house. 

https://www.pinterest.com/explore/carpenter-bee-trap/