"Is there a way to manage the information that Zotero stores without affecting the library?"
Could you clarify that question? But if you're asking whether you can fine-tune what parts of your data are stored in the cloud, the answer is no. It's either Files and data, just data, or nothing.

You cannot sync to a flash drive, no, but you can use a flash drive to back-up and/or transfer your library
http://www.zotero.org/support/kb/transferring_a_library

I believe the default is just data - but you need to create an account and then put in your username and password in Zotero, which means it won't happen automatically, either.
Purging your online data is relatively easy: You create an empty Zotero library (e.g. in a different FF profile) input your Zotero username and password and then use the "restore to server" option in the sync tab of the Zotero preferences. Importantly, though, you need to make absolutely sure to _not_ perform a sync with your regular Zotero profile afterwards, as it will be overwritten by the empty server profile, i.e. all your data will be deleted.

Also, there's no storage quota for data, if that's your concern—only for files.