Best bet may be to go to local dental school clinic where they will finish the work as dental malpractice case may not be justified by damages....

Do I have a potential case?

Perhaps but these cases are expensive to prosecute so unless the damages justify there will be difficulty obtaining counsel. Speak to local counsel...

Can I sue state

You would need to show that the State abrogated a special duty that it had to you (which it did not have). There is no case. Confirm with local...

Car accident..can I be forced to total my car and loose it??

Usually that would be your option. Confirm with local counsel.

Tenant uses bill pay for rent

If it comes from a bank they debit the account as the check is sent to prevent any chance of check bouncing.

If I don't show up to court will the case be dismissed

Contact the curt to withdraw the action.

Can you ask the judge to appoint a attorney for a child who is a year old?

Courts frequently appoint a guardian ad litem for a child.

Can I take this to court?

You can sue him and get a judgment. Collecting on it may be a different matter.

A quote in a publication is libelous. What range of cost would it take to litigate the case (retainer)?

Most attorneys would want initial retainer of 5-10K. Costs to include trial can exceed 40K.

Do I have a medical malpractice case?

No indication of damage occasioned by delay in treatment effectively precludes representation.