1) No, you don't need to do all the side content.
2) Leveling slows down as you increase in level. Doing ALL side content (And killing every enemy) you reach Act 2 at around level 7-8 and reach level 10 by Act 3. It's only in Act 3 when you can hit level 12 early and still have some content left to do (At which point you get to use your full build which isn't a major downside)
As far as the northern part of the bridge... There's a companion to find there, some story to discover and the creche which provides a MASSIVE plot element as well as a plethora of useful items. So... Well worth checking out.
