All good input - compressor and crank pulley.

Have the ac refrigerant checked, just in case.

Crank pulley is a known weak item - the rubber interface in the pulley deteriorates until the pulley fails completely.  The pulley will separate from the hub when this happens.

Have the computer read for error codes. If the CEL came on, there should be an error code recorded which may provide an indication of what cause the light to come on.  Any national parts store should read the code for you - free of charge.

Follow their advice and get the harmonic balancer checked or replaced. I'm not familiar with new Minis, but typically a harmonic balancer consists of a metal hub and a metal belt race separated by a layer of resilient rubber or plastic. If that layer ages or dries out or is overheated, the result would be slippage between the crank and the belt and pulley system. Slippage would produce the burning smell and result in loss of generating effect, crummy a/c performance etc. It might only slip when enough load is applied to it, as when you turn on the a/c. The charging system would function OK with the a/c off.

People at North American are saying harmonic balancer??? Doesn't make sense, I would think it would cause the issue all of the time???

Thanks, I'll look for an answer there.
And yes it blows cold until engine goes into limp mode then I have to turn off.
Did have the charging system and battery checked all ok

Is the ac cold or no? Compressor might shot, as soon as you turn on the ac the compressor clutch engages and if the bearings are shot it will be difficult for the belt to turn and problem arises. 
Maybe the alternator too, if its shot it turns but will not supply power ro the battery then if you turn on ac it requred more power and since the battery isnt charged , it sputters and dies.  if you want to get more repllies about your Bini problem go to Northamericanmini forum, i dunno why they call themselves Notthamerican mini, they just probably wants to be different and sound unique, anyway, give them a visit and youll get answers, here we mostly cater on classic minis, the mini thats slow and leaks oil but loved by many. The new Minis try to immitate the classic mini style but they failed.  Theres only one breed of classic minis,,,not the clubby, not the hornet, not the mini wagon and definitely not the moke... Its the Good ole Classic mini.