1) Baby oil or mineral oil should both be fine. Just make sure it's unscented and I seriously doubt it will ever discolor\degrade.
2) I'd be more worried about the items you put into it discoloring the oil. As long as it's unscented, it should be no more harmful than water.
3) I'd soak everything in a jar of water for a few days just to make sure nothing leaks ink/dirt/lint etc.
4)
Permatex Clear RTV Silicone. You can find it at just about any hardware store. Just make sure everything is the way you want it before using the stuff.
