That's a lot of questions Axman and I guess you will get a few opinions on how to do what you ask so here is my tuppence ha'porth!
Will it be possible to use any of the weeds that I am killing to dig back into the soil - always assuming there is anything left of them - or would it be best to burn them?
The problem here is not the weed itself but its seeds! Have they gone to seed? Have they shed their seeds?
If it is the former then it is a case of burning them.
If it is the latter then you are too late, next years weeds are in place!
If composting them you want a compost heap that gets very warm to do this properly, so overall I would say burn them
I need to break it down fast. So what is the best technique?
Well I look it this way:
The experts will say leave it for around six months to rot down, then dig it in, which is fair comment but I ignore that I dig it in (fresh or not) before the year end (usually Oct-Dec) .
Think of it this way I won't be planting out in that soil for at least six months so whats the point of moving it twice? Its still getting the six months the experts say.
Let the worms chew it up/break it down then when you plant out the muck has absorbed plenty of moisture, and the worms will have created a a nice humus, and best of all is you are not rushing to get your muck in in spring when the weather and soil may not be fit to work in!
bag the ash to use later. Would it be a waste to dig this in before the winter as a way of breaking up the clay, or should I use it as potash in the spring?
Yes it would be a waste because apart from the fact that it might leech away over the winter months,you may happen to plant plants that do not need potash straight away if at all, so yes save it until you need it!
The final third is cover in grass and other less harmful weeds. How long will that take to achieve compost that I can use? I need it asap.
Why? I thought you had loads of horse muck?
and as you are going to have a bonfire on the go why not chuck these on it as well!
Once skimmed, I am covering the cleared land in black plastic to kill off the roots prior to opening it up for digging. How long will the back plastic need to be in place to do that?
Waste of time in my opinion!
As I see it you are keeping the soil relatively warm which is the ideal situation for them to continue growing.
After digging it you could consider laying the plasic over the dug area but not before.
There! I have given you my opinion...Tg