LM1084, should I leave the copper area connected to the TAB floating?
The datasheet should give a recommended layout, but if not then the general rule of thumb is to connect the tab with pin 2, then you can use either the tab or pin 2, or even both, to act as your output.

For instance, this is the recommended layout for a CAT4101 in a 5-pin D²PAK:



And, while it's not the same footprint, the same principal applies to SOT223, as in this recent layout of mine: