It's certainly possible yes, they're often made aware of active warrants and will call law enforcement, they are a government agency after all.
no but you can get arrested at the dmv.
No, although they may not be arrested at the DMV, and they will not be allowed to have their license renewed or reinstated.
If there's been a warrant drafted for your arrest, yes.
No, they just don't grant you your license
yes, see link
No not unless you have a Warrnat for your arrest! LAWL
Depends on what the warrant is for. what if its for child support
If they 'run' your name into the state database to verify your identity and your name comes up as wanted, yes, they can call law enforcement and you could be arrested.
Yes
Yes. If you are a fugitive from the law, then you must first address the issue of your outstanding warrants before you can apply for government issued identification.
Yes, all states do.
In NSW Australia if you have unpaid outstanding fines your drivers licence is suspended until it is paid, If you wait for more then 3 years to do this you will have to sit for your licence again, after you have paid the fines.