The challenges are retroactive, so once you complete them, they are permanently completed even if you restart the level. The idea is that you play through the level multiple times to complete all the challenges, then complete the level for real to get your final score. It's a pretty contrived way to promote replayability. Sadly, if you want to get Silent Assassin on most of the levels, you'll have to complete the challenges as that's the only way to get enough points.
I'm not really sure why they thought it was a good idea to make a Hitman game where the vast majority of the game has nothing to do with assassination. I understand the desire to make it more story-driven and cinematic but they could have done that while still having assassinations in every level. The Contracts mode seems like a band-aid for this. It's like the devs realized that there weren't enough assassination missions so they thought "Hey, let's throw in a mode where players can set up their own assassinations!" It's a cool idea but not enough to compensate for the lack of proper assassination missions.
Hopefully they recognize their mistakes and make the next game more like Blood Money.