E-mails dont take up much HD space at all. How much yours specifically will take up depends on a lot of things. How many e-mails you have, the content of those e-mails, attachments, how long you keep the e-mails, etc. But in general, they wont take up much space.
However, there are a couple things you should be aware of if youre concerned about space. First, Gmail is unique in the way that it uses labels rather than folders. In most e-mail setups, an e-mail only exists in one folder, whether its the inbox, trash, or anywhere else. In Gmail, instead of folders you have labels, which show you all e-mails that are given that tag, and an e-mail can be given as many tags as you like. So when Mail.app sees these labels, it treats them as folders, and so any e-mails that have more than one label are actually downloaded multiple times, and a separate copy is kept in each folder. But again, this really shouldnt be an issue unless you have a very large amount of large e-mails, because individual e-mails are very small.
Personally I only use the default folders 99% of the time (now and then Ill create a Saved one).
As a result of that, the All Mail folder as it shows up in Mail will keep a separate copy of every e-mail you have. The absolute largest this folder will get is limited by the Gmail space limit, which is currently a little over 7 GB, but Im guessing youre nowhere near that (because that would be a TON of e-mail). I dont use the All Mail folder actually, and there is a Gmail Labs feature that allows you to tell certain folders not to show up in IMAP clients if youd prefer (I turn off Starred, Chats, and All Mail for IMAP).
The one other thing you should know about space is that it depends on these settings:
If you keep your e-mails forever, they will naturally start to take up more space over time.
But really, Ill only say it one more time, you shouldnt have to worry about the space they take up. If you have little enough HD space that you cant easily take an e-mail hit, youre in pretty urgent need of a new HD.
Oh, and to answer the other part of that question, theyll be stored both on Googles servers and your HD, so youll have access to them whether youre offline on your computer or signed in to the Gmail website.
As for archiving mailboxes, you shouldnt have any reason to do that. Its not the same as Gmails archive. In Gmail it just means keep it in the All Mail folder. In Mail, archiving a mailbox saves it to your HD somewhere so you can remove it from Mail.app and restore it if you ever need to. You really shouldnt need to archive. As long as an e-mail is anywhere in Mail.app, Spotlight will find it, and find it fast. I actually prefer Mail.apps search to Gmails by a long shot.
As for conversations, it wont work exactly the same. But most e-mail replies quote the text of the original message right below the reply anyway, so you can see the conversation history there. Also, Mail.app has an option under View to Organize by Thread. What this does is lumps all of the e-mails in the current mailbox that are from the same thread together (provided that you dont alter the subject line other than adding things like Re: and Fwd

.
It wont lump e-mails from different mailboxes (so if youre in your Inbox, messages from Trash wont appear there).
Unless youre using Snow Leopard, dont let Mail.app automatically set up your account, because it will set it up as POP, when you should use IMAP. See [URL="http://mail.google.com/support/bin/answer.py?answer=75725]here[/URL] for more information on Gmail and IMAP, including instructions and the difference between IMAP and POP. Also see [URL="http://www.macosxhints.com/article.php?story=20071023233813768]here[/URL] to get Mail working right with Gmails Sent/Trash/Junk/Drafts folders. The last thing Id tell you to be aware of is that if you
do like to use Gmails All Mail, skip that links instructions for the Trash part, because putting an e-mail in Gmails Trash will remove it from everywhere else.