You're going to need a central server to handle this for you. You can't do it at the client level, since you'll need a central "brain" to administer the permissions.
What you choose is going to come down to:
1) Your budget
2) What you need to be compliant with (eg, HIPPA)
3) How your team needs to use the files
Given all of that, you may need to adjust your list of requirements.
I'm not sure what you mean by "should become a junk file if shared elsewhere". I'm going to guess that means if the file goes outside of your allowed zone it encrypts/self-destructs in some way. I'm not aware of any off-the-shelf solution that will do this for you, which means you'd need an existing solution customized or a custom built solution (read: $$$)
Let me see if I've got all your requirements straight:
1) Control access to the file server
2) Control access to the files within the server based on the user's roles & permissions
3) Control this access at the file level in some cases
4) Prevent sharing documents outside of the group.
5) Limit admin privs to a few, select individuals
6) Revision control/audit trails so you can see who did what to the document when
7) local document access on the machine
8) Syncing of files between laptop/server so everyone has the most up to date copies, and of course so backups exist
These are pretty straightforward requirements. Here are some more considerations for you to think about:
1) A determined employee can steal your data. Copy it to USB, attach it in an email, FTP it, I could go on. While steps should always be taken to protect data vigilance is still required. When considering any product consider how it could potentially fail or be misused. Not allowing local copies of files is one way to mitigate this risk, but in many cases it's just not practical.
2) If you use a local file server (one you set up and administer yourself) you will need to consider how you will "harden" it to external threats. Setting up the server and protecting the data on it from your employees will not protect the data on it from people you don't even know.
3) Do your employees need to be able to access this data from outside your office? If so, you will need to again consider #2. That adds another layer of complexity.
4) Do external parties (like clients) need access to this data? If so, you will need to again consider #2.
5) Do you need local file encryption for data at rest? Are your harddrives already encrypted? Because if a laptop gets lost/stolen it's very easy to simply remove the drive, mount it to another machine and rumage around.
There are MANY options for you. You're not the first business to have all these concerns. But which option will SUIT you depends on your actual needs, how your employees work on the data and what your budget is.