Hill phase can be speed work and hill repeats in fact should be a part of hill phase. In fact, personally, hill repeats are the cornerstone of my hill phase.
As for the rest of your questions, it's really a question of what works best for you. This is where training becomes an art. What sequence do you do the workouts in? Some start slow and finish fast, others start fast and finish slow. You just have to find what works for you. Recoveries? Most people do all the fast stuff with full recoveries. Some do alternating recoveries that may involve shorter recoveries mixed with full recoveries.
All types of speed work could definitely be done throughout the whole speed phase. You don't have to think of it as a weekly cycle, though. Maybe it's a 2 week cycle or a 3 week cycle where you do each type of workout once each or most once each and one or two key workouts twice each. Actually, I've been getting to be a fan of this idea. It's what I did this past summer and fall with great success.
You can definitely do 400 meter repeats on Tuesday and 1000s on Thursday. If these are the only types of workouts you are targeting, you could do that through the whole speed phase. Or you could switch to 1000s on Tuesday and tempo runs on Thursday later (or earlier) or you could work hill repeats in. You could even do a 2 week cycle of 400 repeats on the first Tuesday, 1000 repeats on the first Thursday, a tempo run on the second Tuesday, and 1000 repeats or hill repeats on the second Thursday.