I have created a dropbox folder that is shared with my sister. She needs to move the files from various folders as well as delete files (ie edit folder content). Can she do this and/or how do I give her access to do so?
If you share a folder you and all the people you share it with automatically have equal rights for adding, deleting and modifying its contents.
The only difference between the owner and users who joined the folder is, that only the owner is allowed to unshare the folder or to kick out members. Depending on the chosen options, he may also be the only one allowed to invite new users.
Note that changes are only shared for the contents of the folder. If someone renames or moves the shared folder itself this change is only applied for this particular user.