If you're actually using the online version of jAlbum, you can edit the album from anywhere. But if you're using the regular desktop version of jAlbum, that's not possible. The album is created on your PC, then uploaded. To make changes to the album, you need the source files (including the images, the settings, the entered comments, etc.). The source files are on your PC, so you can't get to them from some other location. What's on the server is just the finished product.
No, that's not the same thing. If you're using jAlbum storage, that just means that you're using jAlbum as your web host. You're still using the regular desktop version of jAlbum to make the albums.
The online version uses a now-obsolete version of jAlbum and a handful of skins that haven't been updated in a few years, and allows you to upload your raw images and build the album online. I'm not a fan of it - it has few options, and forces you to upload full-sized images (slow). If you want to try it, go to your profile page (http://kutitomi.jalbum.net) and click Create new album at the upper right. Then click Create now! under the Online jAlbum option.