Now my question is, my husband want to get a time reduction, and is it possible?

Not much. If he did not appeal the sentence there is nothing to be done short of a pardon.

The only avenue of relief is a motion to dismiss in the interests of Justice. Speak with your attorney about making that motion.

What is my most-likely possible outcome? 3rd Degree Burglary and Petit Larceny

Any of those results are possible. It will be dependent upon the judge , the prosecutor, and your attorney. Hire the best lawyer you can afford as...

Is this C summons just a fine or is it actually a reckless driving misdemeanor charge that seriously requires a lawyer?

If it is returnable in Criminal Court, it is charging you with a crime. That is more serious than a traffic infraction. A skilled attorney should...

Summons

For a routine check, no. Certain agencies like the court system, the police, etc can still access the fact of the arrest and disposition.

What are the steps to making this transfer and or is it possible?

There is an interstate compact which allows felony probation to move between states. Ask his probation officer to assist in arranging the transfer.

What steps do I need to take to "adjust" the arrears and get my license back as soon as possible so that I can get a job.

Not sure what you mean when you say "charged the same rate". If you had your license suspended by the DMV, that's where you can get your questions...

In New York why do some people get lucky and get summons while some people get arrested for the same crime or violation

Yes. Not all arrests require the defendant to be remanded and held in custody pending arraignment. If the defendant has Identification and lives...

Arresting question

You do not need to get fingerprinted for a violation.

Arrested vs summons

A summons is not a warning, its a directive to appear in court to answer some kind of charge. Whether that summons is for a civil matter or a...