Can the tablet be powered by a readily available stand alone battery, similar to how I powered the 720 and 740? (I'd prefer NOT to power it off ships' power.)
It's just an Android tablet, so "yes".
But what is your rationale for avoiding ship's power? If because your plane has a very marginal power supply and you need every electron for other critical usage, that makes a lot of sense.
But if your rationale is that you're trying to maintain true independence / redundancy and are separating your tablet power from ship's power for that reason...well, again recall that it's just an Android tablet and is designed for portable usage. Unlike the 7xx devices that did not have their own internal batteries, a fully-charged iFly Aviation Tablet will run for hours on its own battery.
So, charge it before you leave home, then plug it into ship's power during flight so that it remains fully charged, and then if you lose ship's power, the tablet running on its own battery will almost certainly outlast your aircraft's fuel endurance. It will also probably run a lot longer than you'll want to remain aloft without power to your plane's other electrical equipment.
FWIW, I started with a 700 and upgraded to a 720. I had a complete loss of electrical with the 720 when I was only using ship's power, and quickly bought a battery to avoid that situation in the future. But when iFly became available on tablets, I started using it there as my primary source. I long ago retired the 720, and now have a tablet on each yoke, both kept fully charged by ship's power as described above.