Welcome to the forum.
I don't think it matters which group, travel trailer or light weight as long as your here
Can't help with the dump issue except to say I think you're on the right track with 2 hoses and a splitter.
As far as the FW drain, I think you'll find the fitting is 1/2". Take the cap to the hardware store to be sure. You can buy a threaded female 90 to slip coupling to replace the cap. Then a piece of 1/2 pipe to run to the side of the trailer. Add a slip to threaded 1/2" male adaptor and reinstall the cap. You'll want to secure the pipe with clamps especially where you connect to the existing drain pipe and the end at the side of the trailer. I'm sure you'll figure a way for that.
Good luck and enjoy your new camper