The players handbook mentions you move in the 3rd phase, and that magic is a full round action or combat action. There's no phase dedicated to magic, when does it occur, can you move in the same round, and where is it discussed in the rules?
No, I believe the intention is to prevent movement and magic from occurring in the same round. Magic effects occur at the end of the round, after all the rest of the round is completed.
This blog post seems to outline it nicely: http://sordnbord.blogspot.com/2010/10/mazes-and-minotaurs-combat-rounds.html
As magic requires full concentration, and 10 feet per second is a rapid jogging pace (60' per 6 seconds), I'd rule no.
I've allowed a 5' stroll, however... 1' per second is not mentally a distraction, IMO.
Magic is decided upon in step 1 Decision.
It "... will take effect at the end of the ongoing battle round." (RM&M PM p.29) This effectively means that it is step 5 in RM&M.
Note that this is slightly different in resulting meaning from Original M&M... despite the identical wording (M&M p.18).
OM&M Combat Round (M&M pp. 14 and 18):
In OM&M, I've always understood it as "you cast as your combat action." If disrupted AFTER your action, the spell's already cast, and still takes effect.
In RM&M, lacking a combat action step:
Given no point to resolve when they are cast, it implies they are cast when they take effect. Given also that initiative isn't mentioned, that implies simultaneous resolution.
Many do use a step 5 for magic, resolving in initiative order, but the rules as written don't state one, and imply simultaneity. Which way you play can have interesting side effects. Pick one and just be consistent.