I think a 13 mm (1/2") hose diameter is sufficient at most for a very small pressure washer. For larger ones, you need at least a 19 mm (3/4") hose, otherwise the water jet breaks down all the time. The length does not matter, whether it is free or rolled up in a roll-up.

Yes, of course, that's no problem.
Connect the hose, turn it on and you're done

Yes, the Kärcher builds up the pressure. There just has to be enough water (flow) and the hose certainly has that.