Do DropBox favorites sync? Do files I mark as favorites in Dropbox sync across iPad and android phone?  I have marked some photos as favorite on iPad and they do not show up in the favorites folder on my android phone.  

Can I sync them? If yes, how?  I have the app on both iPad and android phone and camera uploads work fine. Thanks.
No. Favouriting a file in Dropbox for Android is like "pinning" in some other software: it downloads the file to the device and keeps it there so you can access it offline. I don't use the iPad version, but I assume it has the same effect there.

Since you might want different files on different devices (for example, you might want a lot of PDFs or videos on a tablet with a bigger screen and more storage to put them on), favouriting a file only applies to the device you do it on.