^^ thats a lot of questions.. heres what I know.. and I may get some of this wrong..

So if Ivy's are in the mix of D1's you have to do your math ahead of time with the financial aid package to see what if any you would get. Yes, that sounds about right
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Ivy's offer the opportunity for a great student to get into an Ivy through LAX when they may not have gotten in? Yes
The crazy race if the dates haven't been moved yet would be Sept 1st and the start of communication.Yes
How soon are roosters completed by the D 1's? this depends on the school, every coach has probably figured out a list of positional needs by graduating year.. and will recruit based on this.. probably don't need a goalie in all grades for example
How much real time does a student athlete have to really give a verbal? after 9/1 Junior year you'll have a few weeks to months depending on the school and the talent of the player..
How soon/late in the talks are scholarships talked about? That is something that will be discussed once a coach tells your daughter she is wanted on the team.
How many official college visits are allowed? I think you get one official visit.. remember an official visit is one in which travel & lodging expenses football tickets are paid for by the university.. . but you can go on your own dime as often as you want
What questions should be asked of the Coaches Schools? the list is endless... but ask about admissions, living arrangements, practice& lift schedule, academic advisers, tutors, GPA. and anything else you are curious about
What should we be asking but aren't? think of things that will be important to you and your family.. social and religious commitments, educational expectations, off campus activities

it seams daunting but it really isn't.. if Lax is what she wants to do it will work out.