It will "remove" them from the "inbox". Continue to read the whole page...you will see that below the place where you set the number of messages and number of day for the mail box "limits", there are three check boxes, and a text field, that determine what happens to "removed" messages, and whether you want to be emailed when messages are "removed" (handled in the way indicated by the check boxes.) "Deleted" means "gone forever"; selecting a folder to put the "removed" messages in gives you a way to set-up a "trashcan" type mechanism if you want (though it doesn't have to be named that).
NO Exactly how you do that depends on how you are managing your mail. Many use POP3 to bring all the messages down onto their computer (using an email client), and deleting them from the server. Others use IMAP and move messages around using folder on the server, other use webmail and leave everything they haven't deleted on the server (in folder other than the inbox). Any of these work, how you decide to do it is up to you.
That said, what you should not do, is to set that "messages in the inbox number" exceptionally high - processing large inboxes is hard on the server, will cause delays for you every time you check your mail, and is just not a good practice. The option for you to "tweak" how many messages, and how old the messages are, allows you flexibility to handle holidays, trips, exceptionally heavy mail load on a temporary basis, etc.
The only safe way to keep "all of your messages forever" is to keep them on your own computer, not on the mail server, and there are several ways to do this - I think using a POP3 client to pull all your mail off the server and store on your computer on a regular basis is the easiest way .
No. The "remove messages" boxes only refer to inboxes - and you can further control whether they apply to only "read" messages, or "all messages" by the use of the appropriate check box that follows.