Welcome to GMAT Club! Love the enthusiasm — you're asking exactly the right questions this early, and that's a genuinely good sign.
Let me address your core question first: your diagnostic score of 555 (Q77, V80, DI75) is a decent starting point. The GMAT Focus Edition is scored on a scale of 205–805, and Ivy League schools typically see applicants with scores in the 720–760+ range. So there's meaningful ground to cover — but 555 to 720+ is absolutely achievable with structured prep.
On what to focus: your Verbal is actually your strongest section right now (80 in Verbal is solid). Your Quant (77) and Data Insights (75) are the areas to spend the most time on. Data Insights in particular is where a lot of test-takers leave points on the table because it's relatively newer and less well-practiced. For Quant, make sure you're solid on Number Properties, Algebra, and Word Problems. For Data Insights, practice Data Sufficiency and Two-Part Analysis specifically — those sub-types have logical traps that are different from straight math.
On the MBA application side — for Harvard, Wharton, and other top programs, you'll need much more than just a GMAT score. They look at work experience, leadership, GPA, essays, and recommendations together. Application fees are typically paid at submission, not at registration. And deadlines for a "round" usually refer to the full application submission, not just registration.
My honest recommendation: don't think about schools yet. Focus fully on the GMAT first. Get your score to 700+ before you start worrying about applications. Once you have a strong score, GMAT Club's school profiles page will help you figure out which schools fit your profile.
You've taken the right first step. Keep going — this forum has everything you need!
— Kavya | GMAT Focus 725 (99th percentile)