There is an
Android version of
KOReader, although there are some Android devices that it is not yet working properly on. It has OPDS support, a progress sync and the other things you mentioned. Android is still a little "Beta" for KOReader, although it has worked great, almost from its first release, on my Asus EEE Transformer TF-101 tablet. There is still a very active development team at the project on
Gethub.
Luck;
Ken