Not an official spokesperson for MRS, but I’ll try to shed a little light:
Is there a clear set of standards for involving MRS?
Generally speaking NH Fish & Game requests MRS assistance if the rescue involves high angle components or extreme weather above tree-line.
Is there a leader? Is it the same leader for each rescue?
The “leader” or incident commander is typically the ranking NH Fish & Game officer or USFS (winter on east side of Washington). There are “Team Leaders” within MRS, but since it is a volunteer organization who is the leader is entirely based on who responds and who gets there first...
Do the MRS guys bring personal climbing gear to use on the rescues?
MRS maintains a lot of gear purchased through donations, and stored at IME. Rescuers still use personal gear, but we are suplemented with gear you would not normally own as a recreational climber/guide (litter’s, long static ropes, rigging, etc). This time of year most of us keep a pack ready to go for when a call comes in, but Team Leaders will stop by IME to grab additional gear based on the scenario.
Once the rescue is out of technical terrain do the government guys "take it from here” ?
It’s a conjoined team effort until the patient is handed off to the ambulance. The relationship between MRS and state/federal agencies is of respect and focused on the mission.
Are MRS W-EMT or WFR?
WFR is minimum, with some EMT's on the teams...
Are rescues conducted in a different manner if the weather is bad?
Not sure what you are asking. Rescuer safety is always first, like any emergency response team. But we are good at suffering and keeping each other safe

For more info on MRS (or to donate) please go here:
http://www.nhmrs.org/