You can access your Zotero library within Firefox. Just click on the "Z" logo in the upper right corner of the browser to access your account on the lower portion of your screen:
Zotero lets you save PDFs, and automatically back up and sync your files across different computers:
Since Zotero stores a copy of your library on its server, you can access the items in your Zotero library from any web browser. Go to www.zotero.org and log into your account to access many of the core Zotero features (such as uploading new references, adding notes, and organizing your items) from any device with internet access, without the need to install any software.
The mobile Zotero Bookmarklet allows you to save items from your mobile browser to your Zotero account. The mobile version of zotero.org allows you to access and edit your Zotero library from your phone or tablet.
No official Zotero mobile app exists, but there are several third party options for iOS, Android, and other platforms.