The floater is one method used to deliver CYA, or stabilizer to the pool. You already have a good CYA level, so you needn't bother with di/tri-chlor, or with the auxillary floater. Just add bleach to keep your FC levels in range.

The CYA is what keeps the sun from degrading your chlorine.

Regarding the empty jugs, what do you do with the rest of your trash? I would rinse them out and dispose of them the same way.