Your understanding is correct. Only one iCloud account can be on the iPad at any given time. And the only way to change to another one would be to delete the one that was there initially, so really not something you'd want to do.
You are also correct about the browser - Firefox does not have a browser version that will run on an IOS device - so no Firefox on the iPad.
Like the iPhone, the iPad is not a multi-user device. So maybe you will need to stick with the Mac.
One suggestion, however, if you are looking for lighter - not sure what type of Mac you have, but if you do not have the Macbook Air, I would say you might want to look into an 11" version of the Air. It is small, light, and very portable....
Hope this helps!