Assuming you're not planting until spring, that should be fine to lay it out on the beds for next year. Just don't go nuts, and add some carbon material as well so it will break down well.
As far as putting it around trees, I don't see any problem as long as it's not super fresh. But I think you'd be better off to throw it in a
compost pile this fall, mixed in with carbon sources, and work it into the ground in the spring to feed the trees. If you're in a temperate climate, your trees are going into dormancy and you don't really want to fertilize them now.
As far as moving things, let them go into dormancy. I'd wait until spring and plant them. That way, you can prepare the new spots now with the pig manure and it will have broken down enough that by spring, when you dig stuff up and water it in well, it should do super well.
If you break the grow cycle now, it could set things back more.