I like the specificity of your questions. This will help us answer you precisely,
I would go with a slightly alternative plan. Take the GMAT as EARLY as you can (of course that will give you enough time to study, because if you don;t get higher it won't count for all that much). Simultaneously if you can, apply to your safe schools R1. And then all the other schools R2. The reason is that to build any reasonable strategy, you need to know your score.
OR, Option B, is to forget about the GMAT. You have a 710. Yes, many Indian students do get higher, but in my experience it's not the GMAT that's hurting you. My feeling is that they told you it's your GMAT, out of laziness to dig into the deep and real reasons. From what I have seen, once you cross 700, you can get into ANY school, and I mean ANY. The rest is dependent on your profile and essays. Of course if you can EASILY get 30 points more, yeah, you should go for it. But if 710 is your plateau, you might be wasting your time.
As for your next question, if you were invited to an interview (not for Kellogg which interviews ALL candidates) then reapply, if you got a straight ding, your chances would likely be a bit better at a different school.
As for suggesting schools, I'd need to know your aims and your profile a bit better, before I could do that.
Best to ya!
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