Is it possible to play both the Oblivion and Morrowind quest lines in one save? For example, if I beat the Oblivion quest line, can I go to the person that can teleport you to Morrowind and start its quest line? Because since you don't start out with the Amulet of Kings in Morrowind, the only other way would be to add the items to your inventory to start the Oblivion questline. This wouldn't be much trouble but I would love to be able to just go back and forth.
Yes. Thermador's transport
Yes.
Thermador's transport mod should take care of all of that for you. No console commands required.