I would guess you have a failed power door lock switch in the drivers door, or the linkage in the door ha fallen apart and does not cycle the switching mechanism. The fuel door locks with the other doors. However, you should be able to open the trunk manually and find the fuel door release handle in the trunk. It will be in the area of the fuel door and a little behind it. Sometimes they are obvious, sometimes you have to search around a little but at least you can get some gas.
For the locking problem, I still think you will find the fault in the drivers door. Either at the lock switch or the lock mechanism. As far as what it will cost, I can't guess what the parts will cost until I know what part has failed and I don't know what they charge in your area, sorry.
Hi. It's there, but they can be difficult to find. The best I could do is this picture of the area where the release is in the trunk on the right side. You may have to remove some carpeting on the right side panel.
If you break it and you need to replace the door, it will probably need to be painted also. If the actuator breaks it will be about an hour of labor plus the actuator motor itself. Your VW dealer can give you the prices on the parts.
Sorry. That is all the information I could find. From what I remember there is just a cable with a loop in the end that you pull to release the door. If you have an owners manual, it should show how to do it better than my repair manuals. Or, you could probably take it to a VW dealership and ask them to pop it open for you, I would hope they would do this as a courtesey. Afterall, it is their product :)
Pull the loop. I will try. Thank you very much. Your patient answering are highly appreciated. Have a great holiday!