1. 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 snappin Microsoft.SharePoint.Powershell dll manually. 

 2. The difference between ISE and standard PowerShell is that ISE got a script editor with highlightning to write code in, while in PowerShell you only get a command promt. I'm sure that there is other features that are different but I'l leave that for google. 

 3. 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 (`Add-pssnapin Microsoft.sharepoint.powershell`). 

 4. Microsoft has done an amazing job to document all the cmdlts for SharePoint so google is your friend here. When you have loaded the dll, you can actually get help from the promt, by start writing an cmd and use tab, and even add the parameter `Get-Help` and `-Example` for any cmdlts available. 

Most of the operations begins with `new-`, `set-`, `get-`, `update-` and `remove-`/`delete-`.

To get all the webapplication titles, you could run

 `get-spwebapplication -limit all -includecentraladministration | select-object title`

[Use Windows PowerShell to administer SharePoint 2013][1]

  [1]: https://technet.microsoft.com/en-us/library/ee806878.aspx