I have 2 different email addresses and I am logged into the one I want to use with iTunes on my phone, however when I try to download an app or update it it asks for the password with my old email address showing. How can I remove that please?
If you go into settings->store->view apple id. You can edit which email you use to purchase apps.
Oh, yes, it is because you purchased the apps on a different account. The apps are not registered to the device, but rather to the iTunes account with which they were purchased. The reason why it is done like that is because if you lost your phone, apple wants you to be able to transfer all the apps you bought to your new accoount.
The only workaround I can think of would be to update the apps through iTunes on your computer with the old account, then plugging your phone into the computer for the updates, if you contact customer support at 1-800-apl-care they can help you transfer the data to your new account, but only call if you have a device that is covered under apple care, or they will charge you. If you can't call go to a local apple store and they'll take care of you.
Hope this helps!