My opinion is first wiring and then painting because there is a chance to get spoil your new painted wall. But your electrician may have an idea to place the LED on a painted wall. You can see here to get a best writing tips.

I'd say you'd remove the old lights, then paint, then install the new lights. Assuming that the new lights are going into the same spots as the old lights.

I'd do the electric on everything except installing the lighting trim then have the drywall and painters do their thing and then install the finished trim (and any switches and switchplates).