Lots of questions...
1) You could use it just as a web filter (a very good one at that) by just installing the web filtration module during the installation and unchecking the other features. Howwever as someone else noted, you could also use FortiGuard DNS (for free) to do virtually the same thing.
Fortinet Secure DNS (malware/phishing/malvertising/botnet blocking)
208.91.112.53
208.91.112.52
2) It DOES include a BB now. In the GUI under settings you will find 'Dynamic Thread Detection using threat intelligence data'. That's basically the BB and you can turn it on in the free version in the GUI.
3) Sandbox aspects are not free. These work in conjunction with their appliances. As Opcode noted, it's an extremely advanced sandbox appliance that works on your network and if necessary integrates into the Forticlient. Without a Fortigate edge device AND FortiSandbox, you won't be able to use these features. However, you will have the benefit of everything else, including the exploit blocker, etc.
4) Exploit, BB (dynamic threat detection) don't use signatures. However Forticlient includes signatures for their other aspects such as the antivirus. By default, extreme signatures and deep heuristics are ON for on-demand scans but OFF for real-time protection. They can be ticked on for realtime under the INI settings posted about earlier. I recommend they be enabled unless you have an old, slow dual-core machine or something.
The benefit of having Fortinet hardware is - endpoint management, sandboxing, localized update pushes, compliance scans and as part of the Security Fabric of Fortinet. Otherwise, the free client does everything else.
As you can see from my setup, I have the full security fabric deployed.