Yes and Yes and it depends....
to answer the three questions you asked.Yes, your bilge pump (at least one of them, if you have more than one) should be wired through the float switch and not through the battery selector switch. This means that as long as you have battery power you have a bilge pump. The float switch is unlikely to short out, and as long as you don't have loose stuff in your bilge to get stuck under the arm, you can count on the pump to start when there is water in the bilge and quit when it's gone.Yes, in the circuit I described above, if the bilge pump stays on (either because of a leak or something malfunctions) and there is no source of charging for the battery, the battery will go dead. Here you have to prioritize between draining the battery and perhaps letting the boat sink.

It depends on how the pump, battery switch and float switch are wired - you can wire them so that the battery selector switch will disable the bilge pump if you choose. Consider, however, that this is one MORE item to check when you leave the boat unattended.Now, on the subject of batteries and unattended boats: it is not good to leave a lead-acid battery without ANY sort of charging, even if you think it is is 'open circuit' because you have turned everything off. There is often SOMETHING still connected, especially in an old boat with multiple previous owners. Even if you pull the cables off the battery - NOT recommended - the battery will STILL discharge at a rate anywhere from 1% to 15% per month.And since a battery's life is measured in 'charge-discharge' cycles more than any other factor (commercial batteries that get little use, like in telecommunications sites, can last 20 years or more), it just doesn't make any sense letting your battery discharge any deeper or more often than really necessary.If you're in a slip, keep the shore power connected. If you're at a mooring, or your slip doesn't have shore power, get a small solar panel (WM sells them starting at about $50) and your battery will last a lot longer.Cheers,Bobs/v X SAIL R 8