Questions about Junior Year GPA

I'm a rising junior at an ivy league school and I have a 3.59 GPA. I'm so painfully close to a 3.6 that i am dying to improve it by even just a hundredth of a point. I know some internships applications open up as early as September with most closing around mid January. My first semester grades will likely be out before Christmas. Is it acceptable for me to wait until those grades come out to submit many(but not all) of my applications? Am I risking too much by waiting until closer to the end of the application period? Also, if I apply, say, in November or early December, can I send in an updated resume to companies with a GPA above 3.6-3.7? Also, is is acceptable for me to list my gpa as a 3.6 or will that be too risky if employers were to find out? One last one...Is the gpa requirement at BBs lower for Asset Management than for other more competitive areas (IB) of finance? Sorry for all the questions, just hoping to get these things cleared up before I start applying in the next few months.