Sidequests do not count towards your reputation, each faction have a set number of daily quest you can do for them. if you open your inventory and go to the goal menu, in the top left corner you can change to reputation and se.
yes it's possible. to view contracts open ego, should be top left under goals, very top of the screen should be a selector to swap between pursuits and contracts. after EGO 250 you should see a pop-up on the left every now and then about collecting ##/100 whosewhatsits from the so-and-so's at the place. there's more types as well, echelon is pvp junk, did one today just had to complete "Motherlode" co-op
The contracts are on a timer. Whenever the timer runs out contract completed pops up and you get rewarded for what you have done. If you do nothing, you get nothing. Press "J" to pull up the goals tab and on the top left you can switch to contracts. That will tell you what you need to do in order to gain rep and how much time you have left to do it. The contracts are automatic and always active, you don't have to go to anyone like you do to activate a quest.
I have done a couple of the cotnracts on the Mount Tam area, but am unable to complete the rampage/ kill count jobs and the time trial. I've been trying to do the protect med supplies with a shotgun and I can't get anywhere near 8k point. At first I thought cool, I can do this with my SAW, but it started with a shot gun!!!
Secondly, time tirial. PAH. The quad and the cars handle like shopping trollies!!! IMPOSSIBLE.