I'm an individual that has an app on the App Store, you can of course submit it as individual (Apple has different developer accounts for companies & "solo programmers").
For sure the copyright of the material is yours, just add a simple message (not really needed, indeed) like "© 2012 John Smith" somewhere in your app to be sure.
Please also consider that anybody can copy your material and/or ideas on the App Store, lots of people clones successful apps there. If your idea is so valuable consider also to apply for a registered trademark or similar.
Your app is free as you said, but if you're trying to get some money from that just be sure to check what taxes you have to pay in your country.