No, there is no way to change the colour of a construction line (or any other line) in a sketch/profile.
No, you can't hide dimensions, but you can hide/show all constraints (Tools > Relationship Handles).
A construction line is just like any other element, so you can constrain it in any way you choose - by applying dimensions or any other relationship such as connect, parallel, equal.
If your sketch is getting very cluttered it may be that the sketch is too complex.
Think about having simpler profiles, even if it means having more of them.
Very complex profiles/sketches are difficult to maintain and will slow down as they get more & more complex, because every time you add a constraint all the others have to be checked. They can also be difficult to solve and fully define.
Are you creating sketches first then creating the feature (as in other systems) or are you creating the profile as the first step after selecting feature type?
SE can work both ways.
In the first way the sketch is not 'absorbed' into the feature, but remains in the tree and can be hidden/shown & re-used by other features.
In the second way (I think most people work this way) the profile is absorbed into the feature.
There are instances where the first way is easier - I do it that way for sweeps and lofts.
bc.
2.4GHz Core2 Quad, 4GB RAM,
Quadro FX4600.