A) Baggage
My best interpretation on multi-carrier itineraries is as follows:
You go on the originating carrier's rules for the segments that are to be flown on that carrier. In her case, you would go by the CO rules for travel to Europe, as that is the extent of your CO travel. I could be wrong, but this seems to make sense.
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B) Check-In @ PHX
Given she has an extensive travel day ahead of her, and missing her first flight could delay her trip by a day (or more), I'd play it safe, and plan on getting her to the airport in the 5:00 - 5:15 range. If she ends up sitting at the gate in PHX for an hour, its better than being stuck in EWR or Brussels for hours or days.
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C) Mileage
As you indicated she doesn't fly *A too often, I'd stick with one single program throughout her journey. Since you indicated she has some UA miles, I would suggest having miles credited to her UA MileagePlus account.
Why you might ask? UA miles are known to expire with no activity, and this trip will keep her small amount of UA miles "active". Even if she has CO miles, they don't expire, and the UA and CO miles will combine at the end of this year anyway.
Her outbound trip is roughly 10,000 miles, I'd presume her return to be around the same. That said, if she should fly 5000 miles domestically on UA, CO, or even US, she'd be Silver on the Combined CO/UA come next year. She'd also earn herself a free domestic ticket.
**I didn't think of this before, but make sure the itinerary she is flying is eligible for miles. Given it was booked through a "student" travel agency, makes me think some unpublished or discounted fares may come into play here, and she may not be able to earn miles.
Hope I've been of some help here.