(1) Your sister-in-law's site is running Coppermine 1.3.2, which is very old. She is strongly encouraged to upgrade because there are a number of security fixes in the current version. It looks like she is using the default Hardwired theme, so she should be able to easily customize the 1.4 Hardwired theme for her site. There are some posts on how to patch the 1.3 series, but that's not recommended.
(2) Users are only allowed to create albums in their user galleries. They cannot create albums anyplace else. Such a permission is often requested and, as a whole, more permissions are being considered for future versions of Coppermine (check the Feature Requests board). There might be some mods that could help you (on the Mods board).
(3) You can set album & group permissions to allow users to upload to certain albums in any categories, but those albums have to exist first. And the permissions are such that the albums are "public" in that once the album is set to allow uploads, all users in groups that are given permission to upload are allowed to upload in any of those albums.
I have the exact same setup on my family's gallery - each couple has its own category and I have an "incoming photos" album in each category. Family members upload files to the "incoming photos" album of the appropriate category, and then I move those photos to a new album I create as administrator. It takes more time for me but significantly less time for them. Usually, they upload ZIP files of the photos which makes it easier for me to set things up. I use the "MassImport" plugin to actually add the large numbers of photos we have.
On
this other thread, you asked about this setup. Now I'm wondering if that wouldn't be a better idea for you. Set up user accounts for each "category" you want, then the "User Galleries" become your family grouping categories. Using the mod in that thread, you can show the User Galleries on the main page. Family members can create albums in their User Galleries and do whatever they like. There might be some issues, but it sounds promising at first thought.