Not if they are fully shielded, which they should be.
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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?Yes....
Should I keep the outlets a certain distance from each other?
I would suggest not putting 2 duplex receptacles in a 2 gang box though. Reason? If you use any equipment that uses a wall wart in some cases the thing will cover part of the receptacle next to it.
How long will the branch circuits be? Distance from the electrical panel? Don't forget to figure distance up and down.
If the wire will be longer than 70ft or 80ft you might want use #10 awg.
I would also recommend solid core wire. Not stranded.
The electrician will hate working with #10 solid wire and probably try to talk you out of it.... If he uses deep old work cut in boxes he won't have any trouble with #10 solid wire.
Breaker size? 20 amp....