Hi there,
Please see below for responses to your questions:
1) Nope, the pre-MBA coursework are not contingent on your GMAT score, so you can parallel track them. However, if you do find those coursework conflict with your study schedule, prioritize the GMAT. While these quant coursework are nice to have, having a solid GMAT score is a must. For these schools, you definitely want a 720.
2) You don't have to complete them prior to the applications. Again, these are optional, but definitely nice to have to show that you're working on your quant skills since you don't come from that background. Telling the school they're in progress is sufficient.
3) Obviously CORe is reputable, but it's also important to weigh you options against your budget. An alternative is taking these classes at a community college for much cheaper. In the eyes of adcom, an accounting class is an accounting class, no matter where you take it (post undergrad).
Another way to demonstrate that you're equipped to handle quant courses in bschools is to get a solid GMAT quant score, which will signal to bschool your potential in this area (ties in with point #1). It is a good idea to take these courses though before school starts because 1) school moves at a fast pace and the courses aren't really designed for beginners, more for intermediate level and 2) it does send the message to schools that you're trying and that will be a good look for you.
Hope that helps! Feel free to sign up for a free consultation if you'd like a more in-depth assessment of your profile:
https://admissionado.com/free-consultat ... sultation/