If it’s not too time-consuming, then why not apply, figuring it is low odds. Maybe you will be pleasantly surprised.
You said your family income (with both parents) is $71,000 with five kids. The income cutoff somebody else pasted above is lower but for a family of four. Your family is MUCH larger.
If the non-custodial parent will not pay, in general, this is no different than the custodial parent also refusing to pay! Colleges, etc are unlikely to respond favorably. But if you have not had contact with the non-custodial parent for a long time and can document that, than go for it. It could be worth the effort.
On the issue of remittances to the “home country”: My guess is colleges and Questbridge will handle this as THEY see fit and it may not be obvious to those of us on College Confidential. If you are able to document those transfers in some way, then it could be worth the effort.
About all of the above - Yes, I know that many posters will disagree. But the reality is that this entire financial aid process is NOT so uniform as many posters will tell you. There is no single formula. There is enormous nuance and variation across colleges (and probably Questbridge) and it is worth your effort to apply, particularly since you will be collecting information that you will need in order to apply to colleges’ financial aid offices anyway. In other words, it is not time wasted because you will need to put together this sort of “financial portfolio” at some point anyway.