@LDX
Many of the questions you asked are things you learn through playing. My favourite cards when I played the Gate were Cabal Therapy, Jitte and Dark Confidant. I'd max out Therapies and cut maybe Geth's Verdicts.
Regarding sideboard, I personally had 2-3 Dark Rituals for combo and otherwise very fast matchups like infect stompy. Dystopias are awesome and I wouldnt play this deck without them @ your sideboard.
Extirpates and Gate to Phyrexia arent cards I think you should spend so many sideboard slots on. I also believe there are better things than Infests, Powder Kegs and Ratchet Bombs out there. You really need to take your time and research what you need. I for example had some Phyrexian Revokers and they did some work ;) They are quite good against Sneak Attack, Griselbrand and Lion's Eye Diamonds if those are popular where you play.
Against burn try to slow them down with discard and drop Nighthawk/or get Jitte'd creature out there. Sideboard out Confidants, Bitterblossoms and some Innocent bloods. Do not sideboard in Extirpates, those are waste of cards, your opponent has his deck full of 3 damage 1 mana burn spells and he doesnt care if you extirpate some away.
I'd also recommend reading Caleb's article on
Cabal Therapy
Card tags are [cards ] [ /cards] instead of [c] + [/c].