The app should be compatible with your phone if you have it on you iPod - I'm not aware of any apps that are iPod-only (there are iPad-only apps, and apps that require full phone capability so are iPhone-only). You are signed into the same account on your phone, you haven't changed countries since buying it, and it's not hidden from the Purchased tab in the App Store app on your phone : http://support.apple.com/kb/HT4919 ?
For thel in-app purchase, not all are redownloadable : http://support.apple.com/kb/HT4009
If you can't redownload the IAP then you could contact the developer and see if your should be able to.