You need to check the admissions requirements of your target schools. Most schools want the GMAT to be complete before submission, so it will be as simple as comparing submission dates to your target test date. Some schools will allow you to submit a score after you submit the application, but make sure you are clear before you proceed, since rarely will any school bend their rules. As for R3 vs. R2 and R1, you are taking a real risk in R3 since there are usually precious few seats left by then and most schools are looking for just the right fit to round out their class. Having said that, applications are down pretty heavily this year, so your odds are likely better this year than most years. Still, your application pool is a deep one as an Indian. Being female will help, though, since fewer females apply than males. ultimately, it is what it is, so they say, so I would just focus on telling a compelling story and presenting yourself in a persuasive way which captures attention. Try to think of how you stand out compared to someone from a similar background as yours.