Submit form data to server side
I don't see any rough mistake with your code, but I would refactor some parts of it.

There are a lot of magic string constants like "AddPProc", "VerifyUpload", "FedAuth". They should be defined as named constants:

private const string AddPProc = "AddPProc";


This code


string url = Config.BaseAPIUrl;
url = url + "AddPProc";



can be replaced with

var url = Config.BaseAPIUrl + AddPProc;


The same thing with the second method.

In both methods there are fully qualified types. It is hard to read this code. For example, instead of System.Net.Http.Headers.MediaTypeWithQualityHeaderValue place using System.Net.Http.Headers; at the start of the file and use MediaTypeWithQualityHeaderValue without qualification. Especially it is recommended for this line:

Proj.Repositories.Models.External.ProcResponse procResponse = JsonConvert.DeserializeObject&lt;Proj.Repositories.Models.External.ProcResponse&gt; (await response.Content.ReadAsStringAsync ());


In this code


if (serviceResponse.StatusCode == 200)
    return null;
else
    return serviceResponse.StatusDescription;



you don't need else keyword. You can even replace this if-else with ternary operator and single return:

return serviceResponse.StatusCode == 200
    ? null
    : serviceResponse.StatusDescription;


getUploadFilesCount is bad name according to C# naming guidelines. Method's name should start with uppercase letter.

This code


if (procResponse != null)
    return procResponse.FilesCount;

return 0;



can be replaced with

return procResponse?.FilesCount ?? 0;


Also it is not good to return string to show that something went wrong. Let exceptions be thrown, don't swallow them. Code that calls these methods should take care about exceptions.

And I don't understand why a space is placed before each ( in methods calls.