Hi, I wanted to know how one can check if they...

We would like to inform you that you should check with the police station or the Ministry of Interior if you have a travel ban issued against you to find out whether or not, and you can also check the Department of Justice through the website: 
travel ban
 and to inquire through the unified number if there is a case or a request to the prosecution.

 the deportee shall apply to the Minister of the Interior to cancel the deportation. This is stipulated in Article 91 of the Executive Regulations of the UAE Residence Law:

Article 91:

A foreigner who has been expelled from the country, in regard to article 23 from the law, refer that he can’t enter the country unless he has a permission from the Minister of Interior, in accordance to article 28 from the law.

And therefore you may by a delegate in the UAE, for being outside if you are the deportee, submit this request to the Minister of Interior.

Your friend shall submit a request of mercy through contacting the Office of the Minister of Interior to cancel the deportation with a request that explains the matter and provide the documents useful for this request of mercy, and this request will be considered through the technical office of His Highness the Minister of Interior, which includes a selection of legal men of the state, A decision in your application for acceptance or rejection based on their convictions according to the reasons of requesting to cancel the deportation.

For visa fees, please check with the UAE Embassy as fees vary from time to time.