Latest attempt to create good compost

Putting in compost accelerator won't do any harm, though I wouldn't think it would do any more good than household liquid activator, which is free and plentiful.
Worms in a compost bin are not usually earthworms, so won't really appreciate being out in the soil.

Leafmould is, in my growing, a central ingredient in seed sowing mix - I sieve it and mix it with seed compost - far too precious for me to use as mulch or chuck in the compost.

If you have too high a proportion of greens, then more cardboard and paper should help - we put it in the compost bin in the kitchen as we go along, and then add more to the bin when we empty it outside.
Slugs will help break the compost down - I wouldn't want to remove them from the bin.

Rats do help make good quality compost - I had quite a tussle with myself, before deciding to move to a rat-proof compost bunker.
I wouldn't worry about using it.

 

Rats that are known/believed to have died from poison should not be composted; otherwise they can be readily added to the heap without regard. Best if the heap reaches 'effective' temperature, (50 deg C is sufficient)