To answer your questions:
1: The advantages of hosting with a provider is that they can provide 24/7 Support, 99.999% Uptime and if the server breaks they just move your site to another. If you are hosting and your server goes down it may take you time to repair.
2:You can use the same or 2 different ones. That doesn't matter as long as where you have your domain you point to the correct name servers.
3:This can be a factor if in different countries but normally this is not a major issue at all. Most large hosting companies like ours can handle all situations.
4:Yes that is correct...we also provide joomla install scripts that allow you to install the latest version of Joomla with the click of a button. You answer some basic questions and it sets up the MySql Database and installs the app.
Hope this helps.