There is no difference more than the UI and that management shell adds the module to use PowerShell cmdlts by default, while in PowerShell you would add the Powershell snap-in Microsoft.SharePoint.Powershell dll manually.
The difference between ISE and standard PowerShell is that ISE has a script editor with highlighting to write code in, while in PowerShell you only get a command prompt. I'm sure that there are other features that are different but I'l leave that for google.
Yes, but the default setting is to run PowerShell scripts in Standard PowerShell. The only thing you need to do is to make sure that the SharePoint Powershell dll is loaded (
Microsoft has done an amazing job documenting all the cmdlts for SharePoint so google is your friend here. When you have loaded the dll, you can actually get help from the prompt by start writing an cmd and using tab, and even add the parameter
-Example for any cmdlts available.
Most of the operations begins with
To get all the webapplication titles, you could run
get-spwebapplication -limit all -includecentraladministration | select-object title
Use Windows PowerShell to administer SharePoint 2013