Paying child support not thru CSA

(Ohio)

When my daughter was born in 2004 her mother and I had to attend an appointment with the CSEA in Ohio because she was receiving public assistance. At that time she declined to pursue child support payment to the surprise of the CSEA worker. In 2006 we went our separate ways. I have always been involved in my daughters life. For a while we split time having her 50/50 until she started daycare/preschool and I began working full-time. I would have her Friday thru Sunday and her mother the other days. Since 2006 I have been paying her mother from $150-$200 per month to assist her financially. I also buy 75-90% of what my daughter needs and she is covered by my medical and dental insurance. In 2007 my daughter's mom had another child with someone else and later in 2008 moved an hour away to a different city to live with this person.

I have continued to pay her every month, along with my increased cost of gas for driving to get my daughter on the weekends. During the last 4 yrs she has worked maybe a total of 6 months. She continues to receive food assistance. We are on good terms and get along, but I want to protect myself financially. Can she pursue back child support if she were to get an order even if she refused support initially? Should I establish a support order myself since I am giving her money on a monthly basis? Should I stop giving her money until an official support order is established? Well, and order is established but I think it only applies to medical coverage. Also, when we were both working we would alternate claiming our daughter for tax purposes. Hypothetically, if she were working, who has the right to claim her on their income tax form? Thank you for any help you can offer.