Does any one know how long it takes to adopt a child in ar. And about how much it cost if the father is willing to sign off his rights?

A lot will depend on the court schedule. Lawyer gets the paper work written in a couple weeks, not sure if your area requires a waiting period from the time they judge rules to the time it is final ( different states have different rules) but a few months should be about average.

Shop around I would say you should be able to get it for 1000 and maybe less I saw some adds for 750 plus court costs, since the father is willing to sign and there will no court fight.

Do a goggle of your state and uncontested adoption.

If the father does not agree, the costs can go well over 5000 and up