Hello solitaire and welcome to mac-help.
Before you can install a newer version of flash player you will need to go over to the adobe website and follow their instructions to the letter. You first need to determine which version is currently installed then properly remove it before installing whichever version your web browser can manage. Make sure you select your OS version (Leopard) from the list as instructions vary for the various Mac OS X versions.
Here is the link:
Flash Player information
Accounts in iChat are found in the iChat menu under Preferences so just add your new account and remove theirs. But because you are using a second hand mac I strongly recommend creating your own user account in the Mac OS to save yourself from a number of minor issues. Ideally you would also want to remove there user account but if you are unable to do that it's not the end of the world. Then iChat and all the other apps will start up fresh.
You can do this in System Preferences ~> System ~> Users & Groups. Just click the +/- to add remove accounts. Create a Standard account for your every day usage. There should also be an account with full administrative privileges but don't use that account for standard web browsing, emailing etc.