1. only if you want to know your ABV and if you want reassurance that your beer is done fermenting. many, many people have done it successfully without one.
2. i'd say keg it when it's done fermenting, after 10-14 days maybe. or if you want to be more sure, wait two weeks since you're not using a hydro.
3. i'm not 100% sure, but if you want to bottle some of it, i'd do that first with a bottling bucket and then keg the rest.
4. it's best if you can start with enough water to compensate for boil-off, but if you have to add water at the end, that's fine and i believe i've read about people adding water as they boil.