Do I have the right to modify visitation?

The only way you can modify a court order is to go to court and seek modification.

Can the father deny me to take my child out of the country for vacations? What if custody hasn't been settled yet?

You should consult with a local family attorney and discuss your situation in detail - but the first suggestion that attorney will likely make is...

My wife has been attempting to file a divorce for the past eight months. She is filing for divorce; the grounds are irritable

No one can answer that question for you other than your wife or her attorney.

Will getting divorce and marry someone else affect my residence ( green card) ?

No.

How to handle a false domestic violence and was put to a restraining order by court. It was filed by wife towards husband?

The husband should hang up the phone when she calls, and call the police any time she shows up.

Family legal advice regarding and absent parent and custody rights

There isn't enough information in your post to give you advice other than that you should discuss the matter in detail with a family law attorney...

How to I go about filing for visitation in California and would my request most likely be granted?

It's unlikely that you'd simply be granted parenting time. Perhaps the court would consider some form of supervised/therapeutic visits, if they...

How can I get my ex husband to give up his parental rights to our children ?

Ask. It's your only option.

It means you probably misread the papers. It would be unlikely to be ordered to submit a judgment roll in a divorce. A judgment, yes - roll, no.

WHEN will I be divorced!?

There is never a need for an appearance in an uncontested divorce. Disposed usually means the divorce was granted. Check in the county courthouse...