How do I go about moving out of state with my children following a recent divorce with me being the primary custodial parent?

You need to follow the requirements of Florida Statute 61.13001. If he is not agreeable to the relocation, you will need to litigate the issue.

When will I receive child support and can I fight for full parental responsibility?

You have to show that having shared parental responsibility would be detrimental to the child. It is a hard burden to meet.

My x-wife filed for parenting modification

No, his income is not considered in your modification.

The 20 days includes weekends and holidays. If the 20th day falls on a weekend, then you have until the following Monday.

After a divorce my wife got 50% of my military retirement. If she remarries will she loose the retirement.

Ms. Jacobs is correct, she will not lose the retirement if it was part of the equitable distribution.

Should I sue?

No, you have no viable basis to pursue a lawsuit.

Do I have the right to tell my husband he needs to move out as our marriage is done as far as I'm concerned?

He has as much right to stay in the home as you do. Mr. Feuerstein is correct, you will need to file a Motion for Exclusive Use and Possession of...

Is personal service required for petition to modify child support?

Your ex will need to obtain personal service upon you.

AM I ENTITLED TO ANY THING BEING A COMMON LAW WIFE

Florida is not a common law marriage state. You should discuss the issue with an attorney in Illinois.

Do i pay support if 17 year old daughter finds job and still in school.

Yes, you still pay support in those circumstances.