For Residency u just have to clear USMLE step 2 and score 90+.Step 1 and 3 aren't necessary.Regarding application date,they start receiving applications from May/June till October/November and all the documents can be submitted online through HMC website.If you are shortlisted then you will be called for an interview that will be held in Feb-March.And if you are selected in the interview then you can start your residency in June-July the same year.Anyways wish you best of luck!