I haven't really seen proposals for planes that are full electric beyond just toys for rich people to do short hops but you might be right that battery planes might make sense with future battery tech. I just don't see anything justifying it right now.
On the subject of energy efficiency though, you're absolutely right. Synthetic aviation fuel is an order of magnitude more expensive than batteries.
What do you mean? I favor synthetic aviation fuel derived from hydrolysis which is very lossy on energy and would largely kill most current air routes in favor of trains. I think a 40x price increase on fuel is likely, but the actual implementation is proven since it's essentially plug and play with existing infrastructure. I think the best way to make up for the subsequent loss of profitable air routes is electrified rail. This tech isn't for getting off oil though, it's for reducing use at best and if it actually does improve efficiency it would be used along with synthetic fuel.