Happy to tell you what my school does, although I've got no idea whether it's "best practice or not".
Basically does your school give the students homework timetables (eg Monday maths 20mins, English 20mins)?
There's a homework timetable, but it's not this specific- it's more like 1hr of science per week, 1hr of English per week, 1hr of history every fortnight (this changes year on year, so these are rough amounts). Not every Y8 student will have say, MFL, on the same day, for example, so having set days would be tricky.
Do the teachers stick to the timetables (days and amounts)?
I think most do roughly, but as I say ours isn't prescriptive on days.
Do the heads of department have any way of seeing if the teachers are sticking to it? Do they (should they) care?
Mine could see what I was setting via show my homework (although I think I'd have to log in for him. My HoD has far more important things (like right now organizing Y11 mocks etc) to be doing than checking up on people setting homework though and he trusts our professional judgement.
We do report on homework twice a year (effort rather than achievement) so if there was no data as none had been set, this would be a problem!
Do they have any way of seeing if homework has been set/marked?
Again, he can check via SMH what has been set. For what's been marked, he could check books. However, most of the homework we set is revision type homework, so it doesn't always need marking.
Do they get any feedback on how individual students are doing?
No. I teach science, there are 900(ish) students studying science between Y7 and Y11 + sixth form. It would be impossible for one person to have oversight of this many students individually. If there are persistent issues with one pupil, things might be escalated to the HoD.
Do they have any way of knowing if the teachers are tracking how students are doing on homework?
Only in terms of checking if teachers are setting detentions- these are recorded via SIMS. HoDs can keep a track of this, but again digging into each detention that has been set and finding out why would be very time consuming and they have more important things to be doing.
Do the teachers have a standard way to tell students about homework (eg all homework is posted on one place on the intranet)...or is it a mixture of verbal/email/other messaging?
We have show my homework- I also tell all my classes verbally. Having a system like show my homework works well for about 90% of children. Some struggle to access it though and new students can take a while to get access.
I do think your expectations of heads of departments are a bit high- most have quite a high teaching load, and a lot of work falls to them. Keeping track of all the students in your department and their homework just isn't feasible. In most schools Y7 and Y8 at least take all subjects- that's usually at least 200 children, keeping track of how they're doing in their homework would be a full time job!
I also think that a lot of teachers would resent being pulled up on things like "why didn't you set homework this week?" or "why did you set homework on Thursday not Tuesday?". If a HoD has hired someone, usually they will trust their professional judgement to an extent unless it becomes clear there is an issue.