There is no version of Internet Explorer for OS X. Here's download site for Safari 1.0 (for OS 10.2)
You'll have to get someone to download the file to their computer & then load it on a USB drive (8GB min). Insert the USB drive into your Mac & copy the dmg file to your Mac. Then double click to install.
However, OWS 10.2 is obsolete & Safari will probably not work with many of today's web pages.
What model G4 is it. In the Menu, click the Apple icon & select About This Mac. I'm sure you can run a much higher version of OS X.
Contrary to the above post, IE for Mac does exist. As a matter of fact, it was the default browser for Mac OS 8, 9, and X up until Safari's release in 2003. It was discontinued not long after that. However, you can still download it here: http://mac.oldapps.com/internet_explorer.php?old_internet_explorer=9. As for downloading Safari, if you're running an earlier version of Jaguar (10.2), you should be able to install it by going into Software Update and downloading all the updates available (provided the Mac is connected to the internet, of course). As for getting Mail back, I don't see how it's gone; seeing as it's a pre-installed Apple program, I doubt someone would remove it, and I'm not even sure it can be removed. Try doing a search in Finder for it. Finally, as for no restore discs, there's really no other way around it unless you get a set of restore discs (which are probably difficult to find considering their age) or get someone to put the restore disc data on a USB drive.
On a side note, I don't recommend using Safari or IE for internet browsing on 10.2. They're so outdated that most sites don't display properly on them. I recommend using the latest version of Opera for 10.2, which you can find here: http://mac.oldapps.com/opera.php?old_opera=15. I have personally tried this on an eMac running 10.2 and though slow (as it is also a very outdated browser version, over 5 years old), most sites seem to display properly (at least, for the most part). Or, as another alternative, I would recommend maxing out your Mac's memory and installing Mac OS X Tiger (10.4) and the TenFourFox browser (link: http://www.floodgap.com/software/tenfourfox/). Do that, and you'd have a rather usable internet browsing machine.