To be honest, I've never gone through these phases in true Lydiard style and I'm not sure his style is the best way to do these (if I thought it was, I would obviously have done it). That said, I'll answer this the best I can and hopefully, someone with more Lydiard knowledge/experience can fill in the holes or correct me if I get something wrong.
I'm going to do this in order of phases so it might be a bit different than the order of the questions you asked.
Phase 2: Hills
Lydiard recommended bounding hills. I believe there is a pretty good description of this at the Lydiard Clinic (check Lydiard Links under the Arthur Lydiard section here for a link to the Lydiard Clinic if you don't have it already). My understanding is that bounding Lydiard-style is a strength workout, not a high intensity anaerobic workout. He did suggest circuits where you would run quickly down a gradual hill on a soft circuit so there would be some short repeats also thrown in but with a lot of recovery.
Phase 3: Anaerobic
I believe you hit Lydiard's philosophy some on this one. His philosophy seems to have been flush the body with lactate in order to teach it to withstand and handle the lactate. I believe he would have runners do longer or shorter repeats based on the length of their race so an 800 meter runner would run 600 meter repeats at a faster pace, while a marathoner might do a hard tempo run. This would be somewhat race specific training, though not precisely.
Phase 4: Coordination
I believe the idea of the time trials was to run at roughly goal race pace for a distance shorter than race distance. This would be some specific pace work, though I'm not sure Lydiard was big on the idea of pace work.
Phase 5: Sharpening/freshening up
I threw in the term sharpening because that's how I always viewed this phase.Pretty much just as you stated, dropping that volume and doing short, quick work for final sharpening. Also, this is essentially your taper so you're dropping the hard work to let your legs rest up and absorb all the hard training.