Electrical – Running appliances during a Power Outage

If you already own the generator I say go for it and try it out. If the generator is anywhere decent then it will regulate the voltage more than enough for a motor so you won't over power the motor with voltage. If the generator can't handle it you will not harm the motor unless you are able to stall it for an extended period of time; the generator shouldn't be harmed either it would be like trying to use a dead battery if it can't push out enough juice it just won't.

The reason I've notice that people suggest higher wattage ones is because they are typically built a little better and since they are capable of more wattage they respond to a peak significantly better, I'm going into peak discussion. Generators supply electricity on demand (even the power stations'), a household generator will produce approximately a few hundred watts at idle, as more items are plugged in/turned on demand rises and the generator senses it and runs harder. Since there isn't a preemptive notice about this, the generator will typically spike/peak higher than the demand and recovery back around what it needs to put out. A motor turning on with capacitors will typically be able to handle that lag, the capacitors will just charge up slower (almost not noticeable in most cases) and the capacitors work as rectifiers handling another other voltage changes during operation. Motors without capacitors also typically handle it but since they don't get a beginning zap from the capacitors you run a small chance of burning out your coils, imagine plugging a 220v motor under load to 110v source it will energize the coils but remain stalled.

If this is a more permanent installation (off grid scenario as opposed to hurricane prep, etc.) I recommend a separate motor starter kit - bad with naming here - before the motor or a heavy duty UPS/Battery system but for just when the power fails I think you'll be fine.

In most cases an extra sump pit is pure plumber profit - if the sump is not tiny, the backup pump can use the same sump, and just be set to come on at a higher water level.

The practical problem with your vision of "a battery with a 110V outlet" (battery charger, battery, and inverter) is that is entirely possible, but wickedly expensive; also, batteries don't last forever, both in the "length of power outage" and the "number of years before you have to scrap them because they no longer work at all" sense, so it gets even more expensive. Sump pumps with a battery backup built in are made - they have many of the same problems, but usually skip the added inefficiency of converting back to 120 VAC and just use a DC pump.

If you have utility water, and such things are acceptable to your utility, the water-powered sump pump has the benefit of being fairly inexpensive to own, being based on a power source you don't have to buy and maintain. You will get a big water bill if you need to use it. If you have a well pump, it's useless.

Anything depending on you running a generator depends on you being home, the generator being functional, and adequate fuel for the generator being available in the event of a prolonged outage - which it often is not, since the filling station does not have power either. You can expensively address most of those with an auto-start natural gas powered unit if you have natural gas available...

You can also use only tile or concrete for surfaces in your basement and not put things that would be bothered by getting wet in it, so that the occasional flood is less traumatic. How badly or quickly it floods if you turn the sump pump off might guide your thinking on this. It can be very expensive to build and maintain a pumping system that will work though a long, widespread power outage.