I'd like to create a service in my application, which creates products listing and updates inventory on ebay using the data in my database. In my understanding you are able to request an oauth application token with using client ID and client secret (ebay) and this way you can obtain a working token without popping up a window to login to your (or user) ebay account and ask for permission. However application tokens are really limited, you cannot ask for a scope for changing products. So you need a user token (ebay) but you are not able to obtain one without showing the ebay login screen to grant permission. Even if I implement the way how it is described, the token expires in 8 hours, so you have to go through the same procedure if you want to do something the other day, or you keep refreshing the token in the background.
So my question: Is there a way to use ebay's new REST api without popping up the login screen of ebay to grant access?
Second question: In my understanding using the old, xml-based trading api involves the same problem, is that right?
Simple answer NO. You will never be able to perform API operations on eBay that involve a seller's account without that seller granting permission to your app. This permission must be granted by the seller logging into their eBay account. This has also been true for the Trading API for many years.