Gmail – Copy and archive every Gmail attachment to Google Drive

Try Zapier. Looks like this Zap will let you save attachments to Google Drive based on a specific label you label your emails with.

Once a file is uploaded can others in my organization see the files and download them as they need to?

You will have to setup sharing options; also unless its set to Public I think others will need to have Google accounts to manage the access rights.

Can I upload and download any file type with Google Drive?

Not 'any' type, but it covers a lot of the common use cases: http://en.wikipedia.org/wiki/Google_Drive#Supported_file_formats

Edit: As @William Jackson points out in the comment below, this is the list of files that can be edited in docs, if you only care about storage then it should accept any file type.