I've moved plenty over the years and find them pretty much indestructible.

I wouldn't move it until it has some new growth though. Then take as big a root ball as you can and water it well in . It should be fine.

Yes, if it's in a pot! Worthy

Even if it is a pot I'd be very careful of moving right now. You don't say where you are in the UK and a lot of Scotland is suffering temperatures below 0˚C and snow. I'd wait until early spring especially if you fuchsia is in the round.