I believe they require employees and volunteers to be at least 16. As to the other questions, be on the lookout. They occasionally put out messages about openings and if you have a skill set they are looking for, you can apply. There was one of those about a month ago.
From the volunteer side, I believe they generally approach members that show a history of helping others and that aren't known for causing problems. As far as I know, they rarely take on volunteers that request to fill the role.
And is it true that the entire company is a front for smuggling illegal colors of Crocs clogs?
+BlargDragon: Lol. I think your right.
Advice?
For the interview, show up in your pyjamas. As often as you can, quote The 3 Stooges. Just before you slam the door on your way out of Eric's office raise your voice and say; "I DON'T CARE ABOUT THE DAM RESTRAINING ORDER, I NEED A JOB!
Hey what are the qualifications for working for Chess.com? How old do I need to be? What must I know? Do I get paid or is it a volunteer job? What program should I use if they hire me? Any and all help would be appreciated.
"Hey what are the qualifications for working for Chess.com?"
If you show any interest in working for Chess.com, you're not qualified.
"How old do I need to be?"
Old enough to know better than to work for Chess.com.
"What must I know?"
You need to know better.
"Do I get paid or is it a volunteer job?"
If you have to ask, you're asking for too much.
"What program should I use if they hire me?"
Just ask around in the forums. You'll get plenty of helpful answers.
"Any and all help would be appreciated."
You're welcome. 
Hey what are the qualifications for working for Chess.com? How old do I need to be? What must I know? Do I get paid or is it a volunteer job? What program should I use if they hire me? Any and all help would be appreciated.