This is a pretty easy project, I suppose. Most of the points below will only require modifications of the existing yapig code.
Please take a look at the yapig gallery to get a better understanding. I recommend you to make a quick install of the software, so that you can see what is already integrated in the admin area of the script. You can find it here:
1) shared login session and user authentification between yapig and vbulletin:
Users should be automatically logged on to yapig, when they are logged in at the vbulletin forum, and vice versa.
(Vbulletin and yapig will be installed on the same domain)
Banned users in vbulletin should not be allowed to upload or view the gallery.
Unregistered users should be allowed to view the galleries, but are not allowed to comment or upload images.
Every user will get a gallery number assigned to them. There is only one gallery per user. The easiest thing is to take the vbulletin user ID as gallery id in yapig.
2) Every user who is logged in should be able to upload pictures in a two step process.
a) Step 1: The form with the multiple image upload fields.
The uploaded images should be added to the users directory. If this directory does not exist, it should be created. The directory name will simply be the users vbulletin user id.
b) Step 2: Entering the titles and a description for every image in an overview (all images shown on one page with fields for the title and description next to them).
This page will have to be programmed by you, because this functionality is not present in yapig. Thumbnail creation is already present in yapig.
No mysql is required, because the information should be stored in flat files.
The administrator functions in the admin panel under "Change gallery" should remain intact. That is, the administrator should be able to change the thumbnail, delete the gallery. check which images should be included in the gallery and change the description of the gallery.
Other functions, like the view count, or the commenting function of yapig should also work.
The user should be able to change his gallery description on a separate options page.
Everything should be programmed in flat files, no mysql.
Comment creation is handled in yapig already. You need to create one file for the description of the gallery in every user gallery folder and one file for the titles and descriptions of the user galleries. You can look up how the comments files are created in yapig, to see how you should create the description files.
As I mentioned: most of the functionality (like the administrator functions, the image upload etc.) is already implemented in the script.