I believe she can apply for SS online, and can do it 3 months prior to when she wants it to start. This is from the SSA.gov website: "The earliest age at which you can begin receiving your Social Security retirement benefits is 62. You can apply for your benefits 3 months before you turn 62 if you want your payments to start at that age"
From Medicare.gov: "When Should You Apply for Medicare? In most cases, you should apply for Medicare when you turn 65. The open enrollment period starts three months before the month you turn 65 and extends three months past the month you turn 65, giving you a seven-month window."
SS checks start ~2 months after you turn whatever age you want them to start. And you get no choice in the date they are deposited. They tell you, and you will like it.
All this info is available online.
Google is also pretty darned helpful. Hope my answer was as well!