Question about superdetailing plastic trek kits

Well said Steven.

You could do a little bit of both. Add to sub-assemblies and also to completed model. I would suggest adding them before painting, as plastic glues to plastic better than paint. Keep parts symmetrical when necessary( like same parts on corresponding warp engines, etc.) And sometimes less is more, try not to overdo the greeblies. Take a look at others' work for ideas.

A lot of modelers attach their' ships to a base with a pipe or something solid. When I'm building I usually have my model attached to the base and handle it with that. I don't know what is provided in the PL kits but you may want to construct a base yourself. A pipe or rod that solidly attaches the model to a fine wooden base would work well. Just mask off the base when building and painting.
With a good base you shouldn't have to touch the model at all, except to add parts.
It is easier to build the entire model and then to paint it, but that's not always feasible. If you have lots of detail that require different shades of paint it could be a masking nightmare. Some parts you'll want to build and paint before adding to the model. You might even want to paint the whole model before detail is added, and then construct and paint subassemblies and add them later.
Just visualize it before building and think of what part might get in the way. Also consider whether a small detail will remain attached if you mask it and pull away the masking later.

I hope this is helpful,

-Dave