1. Zotero currently only allows PDFs. But an old request of mine (and support from several others) is here, asking for it to allow pointing to a directory instead of a file: https://forums.zotero.org/discussion/31697/link-to-directory-for-reference
Personally I organize my references in one directory each (named AuthorYYYY) and then include files (PDFs, scanned images, etc.), notes (TXT, etc.), saved webpages (e.g., publishers website). Easy enough, but not linked directly to my library.
Edit: actually, adamsmith's suggestion seems even better than this! Check that out.

2. You can add manuscripts and other archive types as entries, and they are currently adding more types for the next release (I think there's some discussion of data sets for that?). See the sticky thread at the top of the forum. But I don't think Zotero could actually support editing documents or anything like that. (If (1) were solved by linking to directories, that would be helpful though.)

Yes, I would really recommend OSF for this purpose. It’s easy to use and has been great for my lab.

1 thanks very much for the recommendation of OSF
2 OSF = Open Science Framework