Did a judge Erred when he award a dismissal with prejudice to an insurance carrier for a 3rd party claim?

Lawsuits require properly pled complaints and properly served parties. Any failures there will lead to dismissal of some or all of a complaint.

Do you have to win your appeal first before you can file a law suit?

Consult with an attorney and provide them with the details that are missing here.

How to write a memorandum of law

This is very difficult to do. You need to understand the law, be able to articulate it to the court and do so in a manner which the court will...

What is the purpose of an appeal?

Appeals challenge a lower court's ruling that is legally, or sometimes factually, incorrect.

There seem to be a lot of details missing here. Can you provide more?

Fees to hire an appellate attorney will vary wildly due to the issues presented in the case, the skills of the attorney, availability, time...

In forma pauperis?

There are filings and an order granting you the ability to proceed in forma pauperis. This is not just something you do on your own.

You can appeal pro se, but thinking that you know the process does not mean that you won't fall into any pitfalls. Best of luck.

Should I file a motion or appeal? I was ok with the judges verbal order.

I agree with Attorney Isquith's answer here.

My child support case has been canceled due to my attorneys no show on the court date. I am the mother and baby lives with me. ?

Was the hearing cancelled or the case dismissed? We need additional details in order to assist.