Another dedicated circuit question

Not if they are fully shielded, which they should be.

I don't think that is a concern. I would not bundle the wires together however.

The only suggestion I would offer is that two are on one leg. And that if possible have two outlets that will be closest to each other originate from opposite legs at the breaker box. This will help in case you have some grounding issues in the future you can easily try another leg. If installing new outlet boxes and not re-using existing outlets, I see no issue in having two or all three in a single box. I don't see how they would cause any interaction with each other but if you do have two in one box try to use a left and right leg together in one box for convenience.

Should all three lines be on the same line/phase?

To clarify, I suggest that you have one on one leg or phase and two on the other. I would imagine your electrician will do that anyway based on open ports in your box, but I would still suggest it to him.