Do you have to turn 17 years old to be a Death Eater?

You probably have to be mature so you don't go around eating people.

Nope. Regulus joined and received his Dark Mark at age 16... really quite sad. I imagine many were recruited while still young and impressionable.

No. Draco already had his Dark Mark at the start of his sixth year. It's unlikely he'd turned 17 at that point.

As far as I know they'll take anyone they can get. Wasn't Draco younger when he joined them?