If there isn't a case against you- How come the father of your child can keep the child away from you?

I assume you are referring to some court order you are bound by so have a lawyer review it and retain a lawyer.

If not married to the father and no orders in place then yes she can leave the state of FL with the child.

Do I still have to pay child support?

You have to file a petition to dis-establish paternity ASAP. Use of a lawyer is recommended.

Husband is using the parenting class to hold up divorce, is there anything I can do?

If you have done yours and he has not then file a motion for contempt, it is court ordered. Use of a lawyer is recommended.

Is it possible to request a new family court Judge if he ignores all evidence, recommendations, testimony, etc.?

If you do not like the result then file an appeal to the higher court. Use of a lawyer is recommended.

Is there any way for a 15 year old person to be removed from their parents without their consent

Call DCF if you believe there is an unsafe environment.

What would constitute a substantial increase in pay as pertaining to child support? I.E. 28k per year to 34k per year

that is almost a 20% increase in pay so perhaps you should go back to court. Use of a lawyer is recommended.

Is there a time frame after an order for contempt and enforcement has been signed? I need to get it enforced.

If the order does not impose a deadline then wait 20 days from entry of the order then go back to court. Use of a lawyer is recommended.

I have full physical custody of our daughter. Is her school based on my address?

Check your court order, based on the information you have provided, yes.

If I am married and my husband is going through a custody hearing for previous children from a previous relationship

Your income will not be considered.