Since it has a battery and the battery is (most likely) chargeable, a little loss of efficiency is inconsequential. On the other hand, having an actual physical chain on an electric bike seems indeed unnecessary - at least for less sporty applications, where things like "feel" or precise power delivery are not important. The end result will be a simpler, more reliable bike. Not to mention better looking.
A Tesla motor is 98.5% efficient, so a generator and motor combo being 93% efficient does not sound like a stretch.
If you're riding a single speed bike and the chain regularly derails, then that definitely sounds like a chain tension or alignment problem.
Be careful when you do this so as to not apply too much power when you're trying to do this. If you're in a really high gear and it happens, you can get off, hold your rear tire off the ground and turn the pedals. Works 90% of the time unless you got your rear chain jammed between the cassette and the spoke.
Edit: You can very often see this if you watch professional bike racing. When the mechanics change a rear tire it will almost always knock the chain off of the front chainring. They'll just shift into the proper direct (low if it's off the high side and high if it's off the low side) and then spin the cranks and the chain will come back on.
2. If it's the rear derailleur, it may be bent (especially if your limit screws from step 1 are maxed out). You need a derailleur alignment gauge (or just take it to a shop) to verify.