Vault File Quantity
Two ways really.
Open ADMS, select your Vault, total number of files will be shown in the right hand side pane. This is all files & all versions of those files too, so not really a 1:1 file count.
The only way I know of to get the total number of files is to do an advanced vault search, and do a full $ level search for all files. Criteria something like file extension is not empty, so it excludes folders in the hit count.
That'll then give you the total number of results returned = files in Vault.
Just as a heads up, if you're planning on doing anything like renaming/moving parent level folders... i.e. the highest level folders in Vault, chances are it'll not let you.
If you rename/move those folders, Vault then has to micro manage all the files underneath, if the total number of files to manage in one operation is greater than ~5000 the Vault Client will keel over and die on you.
Always test it on a test server first, ideally of similar spec to the production server.
If it's absolutely critical that you must restructure but the client limitations are preventing it, then you may have to seek assistance from a reseller with the DTU/BCP utility. But that's just a heads up, cross that bridge when you come to it and all that 
No. By $ he means top level in vault. Search for "*".
Here is my search. In "options", select latest version only.
Looks like I have appr 300.000 files, and I do not plan to do any major restructuring/renaming in my vault in the near future 🙂
