Essentially, but you still have to travel the distance in a parallel dimension. Think about layers on a circuit board or road overpasses. You can connect two things separated by something by going "up" in the third dimension, but you still have to actually go the distance after avoiding the collision (and then go down).
No, time has nothing to do with this. The point is that two points separated by an object in 3D space (say, a point inside a box and one outside the box) can be connected by something in 4D space, just like two points on a 2D plane on opposite sides of a river can be connected by a bridge in 3D space.
The time dimension is entirely separate. You always travel a distance in the time dimensions, in space the distance just exists, there is no concept of traveling without time. This is also visible in the math of SR - the time dimension is different from the three spatial dimensions (opposite sign in the distance metric).
Sort of. I don't believe that time is considered a spatial dimension. But from a looser conceptual framework, basically yeah you have to spend some time to travel space.
Also note that even using 3 dimensions to traverse a 1-dimensional space doesn't mean there's guaranteed to be no distance between two points. A string can be super densely coiled in 3D space where there's basically no 3-dimensional distance between two points on the string, but it can also be stretched out or loosely crumpled and still have lots of 3d space between two points on the string.
