For dangles, you'll want to use a topology, but a straight out of the box 'Must Not Have Dangles' rule will make you crazy when it comes to cul-d-sacs. Take a look at this post from friend and colleague Tim Witt. I used the original add-in and it worked great!
As far as editing roads as per your illustrations: get ready to roll you sleeves up and get your hands dirty. It's a boat load of work, but the end result will be worth it. Personally for roads, I'm not a fan of anything but true intersections with a couple of exceptions, and this is based on my work in 9-1-1 dispatch.
I routed response vehicles across my centerline data and used intersections only rather than vertex: There is a lot of data out there that evolved from the old ESRI Coverage model where anytime one line crossed another there was an intersection. Consider the case where a surface street over-passes a freeway or other limited access highway. In the coverage model, there was an intersection where they crossed. Fast forward to the Geodatabase model; that same data may or may not represent that line crossing as an intersection; it may represent it as coincident vertexes. Image my chagrin if I allowed a route to follow vertexes instead of true intersections and routed a fire truck off an overpass to the underlying freeway...
However, in the street centerline feature class we included several pedestrian only trails. For 9-1-1 dispatch purposes I couldn't route a vehicle down a trail, but if someone else wanted to use the data for a walking network, there needs to be connectivity. I added a vertex on the street, and snapped the trail to it: connectivity, but not route enabled for my purposes. (Since I was the manager of the data, I got to set the rules of the game...)
Hope this helps-
That should just about do it....