Hello,
I don't work for
MGMAT (I work for Veritas Prep), but to answer your second question: Assuming they start early enough (which you're doing), I always recommend that applicants take the GMAT early enough so that they can take the GMAT twice if needed. And, you ideally can get the GMAT out of the way before you work on the rest of your application.
So, working backward from early October, you want to finish the GMAT no later than early September, which will give you about a month to fully focus on the rest of your applications (esp. your essays and letters of recommendation). Taking the GMAT in July would give you more than a month to study and retake it in early September. Assuming that it takes you 8-10 weeks to properly prepare for the test, you should start your prep no later than mid/late May.
Ideally you won't need to take the GMAT more than once, but since you're starting early, you should definitely build into your plan enough time to take it more than once. You could even build in time to take it three times, but I think two is a safe number. If things go horribly wrong with your first two GMAT attempts, you can always take a step back, take some extra time to take it again, and apply in Round 2 in January. That would be smarter than applying in Round 1 with a disappointing GMAT score.
Good luck!
Scott