Hi. I'm tjg1, the main developer of Nori/Norilib. I've recently decided to expand the scope of the project to make it more of a general-purpose image search engine (not just for boorus). I've added support for Flickr in the last release and support for more sites is on the way. Tell me what other sites you would like to see (email me, or open a GitHub issue). If you fancy doing a bit of coding yourself, adding support for a new API type to Norilib (Nori's API client library) is very easy. Take a look at the Flickr code for an example: https://github.com/tjg1/norilib/blob/master/src/main/java/io/github/tjg1/library/norilib/clients/Flickr.java
Things like sorting are very much dependent on whether the API used supports it. I did not want to add it for booru, because sorting on sites like Danbooru takes up one of the tags out of the maximum number you can search for as a free user. For sites like Flickr, I guess it makes more sense. You can download single images in Nori, but there is no support for mass-downloading. It could definitely be added.
Oh, and by the way: Nori is back on the Google Play Store: https://play.google.com/store/apps/details?id=io.github.tjg1.nori . I still recommend using the F-Droid build for boorus, as I had to lobotomise some features (adult image filter, auto-complete) in the google build to make it compliant with the Play Store Content Policy.