Telerik: this is because the coded steps are in the context of the Custom class you created. If you move them in the class BaseWebAiiTest and the proejct is configured for it, then they will be shown in both Test Studio and Visual Studio without any additional setup. If you want to use a custom base class for some reason, you have to take care of defining it properly and having the coded steps in the proper class.

Telerik: using 'BaseWebAiiTest' as code base class will ensure you can use both Visual Studio and Test Studio with coded steps without any additional changes needed. Using Custom base class seems to have specific behavior in the two different IDEs.

Telerik: you have to include the full path with namespace in order for it to work in Visual Studio only.

Telerik: this is hapenning because you have changed the Test Studio project code base class 'BaseWebAiiTest' to 'CustomWebAiiTest', which does not inherit the original and thus the coded steps cannot be resolved. In order to fix your code so you are able to see your coded steps, you should do 2 steps: 
1. in Test Studio project settings Recording options, use the full path to your custom base class, including the namespace, i.e. 'CRM_Autotests.CustomWebAiiTest' ; 
2. generate in the project an independant class that defines the inheritance of your custom base class from Test Studio 'BaseWebAiiTest', i.e. 

using ArtOfTest.WebAii.Design;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace CRM_Autotests
{
    public class CustomWebAiiTest : BaseWebAiiTest
    {
    }
}