1. Yes, that's fine. Be advised though that both have an expiration date - the medical exam is only valid for one year and the police check should be submitted within 3 months of being issued. So try to get them as late as possible.
2. Yes, New Delhi would be advisable. They usually process very quickly. India has a thing about passports though, they will not send them outside the country. So whatever you do, don't have her send in her passport while she's still in the US. She'll have a hard time getting it back.
3. When you do the medical exam, be sure to tell the DMP you will be applying through New Delhi. They should send the results there instead of Ottawa, where they would normally send them if the processing was done in Buffalo. If they need an address, you can find it here:
http://www.cic.gc.ca/english/resources/publications/dmp-handbook/appendix-01.aspI don't think there will be any issues.