proxy and app filtering

Because proxy works on HTTP connect method we can do web filtering but if an environment is running a proxy network using fortigate utm then how would we do application inspection ? Because in proxy config we can only apply web filter profile and not application filter profile.

another question

If we configure the network as proxy using FTG it is clear that we are terminating the session on FTG and not on destination IP because we have proxy IP in the browser. If we are doing HTTPS inspection would we still require that deep packet certificate on each client PC or it should work without that.