Are you logged into your site in the app? I can see the button (although I never use it since I use physical albums) in the bottom right-hand corder next to the Home icon. You also need to be in an album to upload it looks like. If you're at your root level, the button there is to add a new root-level album.

Weird, not sure. Have you tried deleting and re-installing the app? Maybe there's some privacy setting or something that's blocking it?

Well, that was somewhat self-inflicted. I grep'ed through the admin php files and discovered that the upload functionality is turned on for users with "Webmaster" role. I changed it and now I can upload.