1) Would you have to have an extra power supply for the light up toggle switches, or would the power from the guitar be enough?

2) If you use a 3 lug toggle, can you just bypass the ground, or do you want to use one hot lug and the ground?
I think you could probably use the power from the same battery if you already have active pups or other electronics in there, but there's not really a "power supply" in a passive guitar- the pickups more or less act as really weak generators to send miniscule amounts of current down the lead, definitely not enough to power any kind of light.

No idea about your second question.
Dunlop Straps™
The best sounding straps on the market

Quote by steven seagull
Justice is this, justice is that...justice is 9 minutes long and recorded in a cupboard full of fluffy pillows