Should I attach the fence post(s) where my fence meets my house? How do I do it?
Don't attach the fence to the house. Aside from putting holes in your siding (not a good thing), your fence and your house will most likely move differentially. The attachment could result in a tear of the siding, which would be a bad thing.

Place the fence post close to the house, then run the fencing top and bottom supports up to within an inch or so of the siding (do leave a little gap, for that differential movement). Place the slats on the supports, allowing the slats to get just a bit closer to the siding.

You could even install a flexible membrane, similar to a product used to seal the bottom of a garage door at the floor, between the fencing and siding.