If TMP is going to get a remaster at some point, then 4K would make sense at this stage. However, rendering the CGI DE effects at 4K would be quite time-consuming. I'm not really up on all the technical details involved in all this.
That depends on how precisely they decide to do it. The software used for the 3D in the DE has evolved considerably since 2001, to the point where just loading the files up would make them look terrible without a considerable amount of reengineering, and with modern rendering techniques, there might be a notable difference in render times at the different resolutions.
On the other hand, with computer power being what it is, if they loaded the files in the version of the program they were made for on a modern CG workstation (never mind a modern render farm), re-rendering the scenes in 4k would probably not take too much longer than rendering them in 2k. It'd require more memory and storage to work with, of course, but that's a drawback of 4k in general. I'm traveling for the holidays, or else I'd be tempted to run some of my oldest scenes from the turn of the century to get an idea of how much faster things could go and how different 480, 1080, and 4k render times would be on them.
Ideally, they probably would retool the CG a bit to take advantage of advances in the state of the art, but if (and I emphasize "if") all of the working files are still available from the 3D and compositing, since all the fine-tuning had already been done to get it to look like vintage 1979 work, I'd probably just go with digging out the old software and putting out all the old effects as-is rather than, essentially, redoing all the additional effects of the DE from scratch (even though there are aspects that would benefit; the step-printed animation that isn't actually period-accurate, some low-resolution areas and notable inaccuracies in the Enterprise model, that extremely slight off-axis camera angle in the wormhole sequence, and some of the matte lines and bleed-through in the drydock sequence would be easy to touch-up).