The only issue I can think of might be in regards to turn-signals if you change the tail-lights: you might have to change the flasher. But markers? No problem.
Flasher's require a resistive load, and LED's almost draw nothing. But, if the tow vehicle has standard incandescent turn signals, you'll have no issues at all. Matter of fact, if you convert your trailer, it prevents ever over-loading your circuits. I've seen trailers with so many running and brake lights, it's a wonder the fuses don't blow all the time!
Exactly. They make a few aftermarket flashers that will compensate for this.
Or, you can "ballast" it with a few resistors. Resistors are likely the only recourse if you've got a small microprocessor controlling everything that is "expecting" a greater load on the circuit - as someone noted with their Cayenne.
Ah, technology: what would we ever do without it?