With your current profile, I’d consider the schools, especially Yale, to be very high, possibly unrealistic, reaches.
Your GMAT score would be OK for all these schools except Yale, IF you had a strong GPA. But the slow career blooming plus the relatively low numbers together make these schools too high a reach, I believe.
To answer your specific questions:
1) It would help; alone it wouldn't be make or break, but together with the things mentioned below, it would enhance your profile.
2) You must explain the low GPA, and it may help a bit – especially if they know you were working during school, which is always challenging.
3) I definitely suggest taking classes and earning A’s – it will show academic capability AND commitment to your plan AND maturity to address a weakness.
4) Raising the GMAT by 20-30 points will help, if you ALSO do the things suggested above.
Overall, if you do ALL these things, I believe you would be a viable applicant to all the schools you mention except Yale (where the GPA will carry a bit more weight)—they would become
reasonable reaches.