Siding corner and roof vent cap question

Hello,

Looking for an advice, in reference to the attached picture:

1. There is an uncapped hole of the siding corner through which rain water is getting behind the siding.
   What would be the right way to cap it?
   
   
2. The roof vent cap looks old and rusted but no leaks. What would be a better maintenance approach at this moment, to complete replace it or just to caulk around and not disturb a fairly new and good shingles?

Thank you in advance!