Is a second career in statistics and science realistic? Accountant inquires
Not too long ago I faced the same issues as you. I wanted to go from economics to software engineering, particularly machine learning. I'm in a department with a decent emphasis on statistics, I know several future PhD statisticians, I have a general idea what those groups look for. 

1—You don't want a masters in applied statistics (MAS). You want an MS in statistics. Huge difference. A graduate student in my department got an MS in stats from a top-ranked stats school that also offers an MAS. He said what he teaches in undergrad math stats is above what the MAS students learn in their first semester. If you write a thesis for your MAS, it will probably be a data analysis paper, not a minor contribution to the field like you would for an MS. The MAS degrees aim for people who don't know much about stats, and they mostly emphasize how to do things like statistical programming over original contributions to the statistics field. You get an MAS to go work in industry for a PhD, not to go on for a PhD.

2-I hope and suspect that your age won't count much against you. My department regularly admits people in the their mid-to-late thirties, as well as 22-year-olds. But we focus on applied mathematics and like to industry work. Again, you should get an MS instead of an MAS.

3-It can't hurt, but may raise eyebrows. Don't count on getting in with a biostats researcher, however. There are some security issues, and grants sometimes restrict who can access data for a variety of reasons. 

My unsolicited advice: start to bail on accounting now. Start a second bachelor's degree in mathematics or statistics. That gives you a better shot at graduate school and a foot in the door for a stats graduate program. When you get into an MS in stats, go. Don't do it part time, go full blast, finish and get into a PhD program. It's a good time to get into statistics. When you finish, hunt for consulting gigs or go a route like machine learning, and you'll more than make up the lost accounting salary. What you'll never make up is the time.