Do grandparents have a right to see their grand children in the state of florida?

Grand parents have no rights in FL so you have no case.

Is it true there is an 18 month waiting period between parenting plan modifications?

The burden of proof to modify a parenting plan is substantial, material, unanticipated change in circumstances.

Yes you can do that however that is a generic order, it is better to get a more specific personalized order to your case.

I want to divorce and not pay alimony. My wife is getting laid off. Should I wait until she is employed again first?

Alimony is based upon need, ability to pay, and length of the marriage. You may as well file now get it done courts are slow.

Do I have any financial responsibilities towards estranged husband?

If you have been married a long time you may have exposure to an alimony claim.

Is there any other way for me to get my child's father served with paternity papers?

Internet messages is not service of process. You have to get personal service so you have to locate him first.

After 2 mths of seperation, parent requested a 60/40 split but it is only taking 75/25 w/no formal agrmnt. Will court go 75/25?

It is ultimately up to the court. It is based upon the overall best interests of the child.

I have a family member living in a home that I own in Tampa. I live in England. He has no lease and pays no rent.

Give a 7 day notice terminating the tenancy then file a petition to evict him.

Wait for my counter petition to be heard before asking for final order on opposing party's petition?

Set your matters for hearing, do a notice for trial first.

Can i set the time and place i want my daughters dad to pick them/drop them off??

Yes, if you cannot agree as to a pick up time and place then have it spelled out clearly in a court order.