Should I attach the fence post(s) where the fence meets the house? How to do it

Last summer we rebuilt our fence using advice from The Fence Bible. The advice was great, and the directions clear. The author covered both concrete and compact dirt/rock footers for wooden fences. I'd highly recommend it to anyone building a fence for the first time.

Concrete does risk rotting the wood because of water build up, but that can be mitigated with proper drainage. Dirt footers can be problematic if you have very loose dirt in your yard. Dirt requires lots of work with something heavy to compact it; concrete requires mixing and handling concrete.

We set ours in dirt/gravel and realized it was exactly the right choice when our fence was hit by a car 4 months after we built it. The car shattered two 4x4 posts, a gate, and several rails, a 3rd posts was pulled from the ground, and every other post along the run tilted about 5 degrees including a 6x6 corner post; 10 posts had to be reset in all. Our neighbor (whose fence was also hit) had concrete footers, which were pulled from the ground, or shifted several inches but left in the ground. His footers had to be removed and replaced, and all new posts were required. We had to replace the damaged parts (2 posts, a gate and several rails), but we could reset the others. If we'd had concrete I suspect more would have broken, and we would have been unable easily reset any that had tilted (granted fewer might have tilted but that energy had to go somewhere, hence the assumption about more broken posts).

Eight feet is a common distance between posts, due to it being a standard lumber length. You will have a stiffer, longer lasting fence at 6-7 ft. An integer number of pickets with your desired spacing is a good way to decide from a design standpoint.
I prefer to sink posts to at least frost level (42" in my area). The 1/3 advice is good if frost is not an issue.

I also prefer crushed gravel (21AA or paver base) to place wooden posts (versus concrete or pea gravel). 3-4" in the bottom of the hole (beneath post), continuing up the sides of the posts to just below the surface. Give the post a push after first 5" and tamp along all 4 sides as you fill. This technique will greatly extend post life and minimize rot.

I've used the gate brackets that you build into the gate which have hinges built in. They will stabilize a 42" gate (each side). Extra long screws on the top hinge are helpful. Stainless steel cable run diagonally (with adjustment turnbuckles) run from the top of the hinge to bottom of the gate (at the opposite corner) will make it sag proof.

Disclaimer 1 user of product, no financial connection:

Disclaimer 2: Haven't used it but sounds interesting, YMMV (Near) Instant fence post backfill