Can I use a USB hub to simultaneously charge a tablet and connect a USB drive?

No, what you "want" is not that simple. Most hubs are not designed to conduct the current backwards from downstream ports to upstream. Even if some cheap hubs do have the direct connection, the tablet will not recognize the cable as a charger cable, will continue to be in HOST mode (which means supplying VBUS, not consuming), and obviously will not charge itself. So the case (2) will not work for this reason.

In case (3) the tablet will take charge as from a regular 500-mA port. However, there will be no any USB connections.

To have your tablet to be charged and simultaneously be in host mode, a special arrangement is required. In USB charging specification it is called "accessory charger adapter". For some more details you can see this item. However, your tablet must support this "accessory" mode, which may not be the case.

ADDITION: The devices are available at Amazon with keyword search [OTG and charge at the same time]

You can purchase USB Hubs (example) that will provide sufficient power to charge a tablet. Do not plug a charger into some random hub, not specifically designed for that purpose, it almost certainly won't work, and many fail catastrophically.