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Quest specific enemies level up as you do, so the only real benefit of waiting will be your combat effectiveness and possibly the quality of any rewards / drops.

Stealing and murder quests are part of the Thieves Guild and Dark Brotherhood questlines (respectively). Doing them earns you Infamy instead of Fame (if you care about that), and they are completely separate from the main questlines. Do them or not... they shouldn't affect the rest of the game (except possibly some NPC reactions / conversations, and the ability to use Wayshrines if you have lower Fame than Infamy). I wouldn't do both the TG and DB quests at the same time though... it may screw up your TG questline.

If you want to clear your good name after obtaining Infamy, there is a way with the KotN add-on (a pilgrimage).

Big hint: find Azura's Star (helps with Soul Trapping).