You can indeed install both versions of Office on the same system, without any licensing implications.
Regarding Outlook, you can only have one version at a time (unlike the other Office apps) because of the way Outlook works, so you'll have to choose whether to remain with Outlook 2003 (and its PST file) or upgrade to Outlook 2013, with the consequential PST conversion. Of course, if you make a backup of your PST file, you'll still have the data as of that date available should you decide to revert to Outlook 2003 at a later time. AFAIK, though, there's no conversion path from Outlook 2013 back to Outlook 2003's PST file, so any later data wouldn't be accessible (unless you're using, say a gmail account, in which case you can re-download it from there).
Cheers
Paul Edstein
[MS MVP - Word]