You should be able to notice a difference any day now.
Always better to sow seed than it is to turf. Turf you need to make sure there are no cracks in between the turf and water it more often. Seed you just water and fertilize.
The grounds man won’t cut the pitch in the winter. No growth, so all he will do is repair divots and roll the pitch. The average height of a football pitch is around 22mm as far as I know.