Is it a violation of probation if my cousin is on felony probation in one county and then charged again in another county?

Committing a new crime is a violation of probation regardless of the county.

Yes you can get charged. Better hope the authorities don’t find out.

Can a prosecutor press charges against someone? even if i say not too?

They do not permission from anyone. Yes they can press charges without anyone’s consent, they do it all the time in domestic violence cases.

You are not required to pick up the subpoena.

Because of the sensitive nature of these accusations I’d suggest you exercise your right to remain silent. As far as evidence needed, her word...

What will happen when I try to cross back to the us from Mexico on probation?

Depends on the terms of your probation. I would suspect most federal grants of probation require that you not leave the country without permission

I was I was arrested got a DUI misdemeanor never convicted. Never received anything.

An important question is how long ago did this occur? Is it past the statute of limitations? If so, and you were never charged, then you can...

Can i get in trouble?

No you cannot get in trouble, however he can as there’s likely a restraining order. And sincere he’s disobeying a court order it’ll only be worse...

Can you successfully fight a ticket that was issued on private property?

Not based on that argument. Officers are permitted to give ticket in such locations

Is there a statue of limitations for an open container on the beach?

You can probably beat this case, however you’ll need to hire an attorney, it won’t go away on its own.