TL;DR: Yes, and yes.

Annotations from PaperShip are saved directly to the PDF file, so they are synced accross devices, and readable everywhere. Please note that the official Desktop app from Mendeley uses a different kind of annotations (closed to third-party developers). We hope a future release from Mendeley can improve that.

Regarding Zotero, we just started working on it! There’s still a lot of work, but it’s definitely on our roadmap.

Thanks for the interest!