You are absolutely allowed to visit other resorts. You can dine there, you can shop there, you can rent boats from the various marinas, you can even sit at the pool bar there and order drinks. You can wander the grounds, and even wander the pool deck, but you can't swim in the pool if you are not staying there.
As far as transportation, there is no "resort to resort" transportation. We generally stay at the Value Resorts. We do visit many other resorts. We usually go there for lunch or an early dinner. How we do this is take the bus from whatever theme park we are at to the resort we want to visit. We have lunch, we then wander the shops, we then wander their pathways, and then catch a bus back to whatever theme park we want to spend the afternoon/evening.
We love spending an early evening at the POFQ Pool Bar. So we make it a tradition on our Animal Kingdom day (which closes early) to take a bus over to POFQ. We then have a few drinks at the bar there and chat with the bartender. We then take the boat to DTD and have dinner, then go to Pleasure Island, then take a bus back to our Value Resort.