Can petty theft, initially classified as a misdemeanor, that eventually led to even greater pecuniary damages, become a felony?

In CA it becomes a felony if the value of the item(s) are more than $950.

He won't come home first, he will be transferred to the facility.

Have you asked your probation officer about it? Your probation officers opinion will be important to the court in deciding whether it's OK. Also,...

Formal misdameanor probation.

Violating probation will subject you to jail time. Get a court date and ask the judge for permission to leave.

Terms and conditions

It means if you leave CA without court permission before you leave! you have violated probation. Probation violations can result in jail time.

In California: I have three unpaid, overdue, traffic tickets (cell phone, stop sign, and crossing a double yellow line).

Have you been convicted of them? If you haven't been convicted, you can't appeal. If you have waited too long, you can't appeal.

How can I file a lawsuit?

This is not a criminal defense question. Try asking this in a civil lawsuit arena.

I have long standing dui warrant. Will that be cause for arrest when entering US?

Yes it can. Get a lawyer to help you get rid of the warrant before you travel.

Can the police use search and seizure claus on informal probation to avoid getting a warrent if they suspect you of a crime?

If he was on search conditions, then they can enter at any time and search without probable cause. They don't have to tell you anything...

I have long standing dui warrant. Will that be cause for arrest when entering US?

It certainly could be. Why not take care of it before crossing the border? Sometimes attorneys can get the warrants quashed with a promise to...