Re: 3rd dwi - probation violation, out of state DL revocation
"Probation" refers to the court's "stay of imposition" of sentencing, or "stay of execution" of sentence, where "sentence" equals jail or prison time, and the "stay" means a forbearance conditioned upon your meeting whatever conditions the court has set.
If a person fails to comply with probation conditions, normally the probation officer forwards a request to the judge for an "Arrest and Detain Order" -- essentially a body-only arrest warrant. Generally the only way to clear the case form that status is to turn yourself in to the jail, and go before the judge for an initial probation violation proceeding appearance. The matter could be resolved then, often by negotiated settlement, or it could be scheduled for an evidentiary hearing at a later date. In the meantime, the probationer may or may not be released form custody -- most often, not.
Whether you can get your case out of active warrant status in Minnesota without serving jail time is impossible to answer based upon the hypothetical given. As a defense lawyer, the only way I could make that determination would be if the person hired me and I attempted to get the probation officer, the judge and the prosecutor to agree to that sort of resolution. It seems unlikely, and challenging. But, what has seemed impossible has sometimes turned out to be possible, with enough effort.
As for getting an Arizona drivers license, all or almost all states in the United States are part of the Interstate Compact on Drivers Licenses, and will refuse to license a driver revoked in another state. Therefore, you will probably need to get Minnesota's Department of Public Safety to out your drivers license in "valid" status (by meeting their conditions), before another state will license you.
You can call me to discuss further if you like.