1) That stuff at the bottom is yeast, the same strain you fermented with in that batch. If you want to reuse it you can pitch onto it (which is often times over pitching), or wash it. Instructions for washing can be found in a number of places.
2) You can make a starter from dry yeast, but it is in quantities great enough to inoculate a five gallon batch from just one packet. Typically rehydration is all you need with it. This is all stuff I have read, I have never personally used dry yeast (im a sucker for those smack packs and viles).
3) Starter gravity should be 1.040, and the volume depends on the gravity of your batch but I just go with a 1L starter for pretty much everything. Start it a few days before brew day, let it ferment the starter wort, stick it in the fridge for a day to let the yeast flocculate, then decant most of the liquid and pitch.