I have 3 machines - one which is IIS, one with a database and one from which I test the efficiency of my application - which means: Using The Grinder I run 1000 instances of my application (hosted on the IIS and operating with the database on the machine with SQL Server). And using perfmon I observe that there really are 1000 requests.
BUT the problem is that connecting to this application (IIS) from another computer is very slow. I suppose there is some bottleneck on the IIS side but I cannot find it - CPU usage is less than 10%.
I think I changed every option in the IIS Manager and machine.config and web.config files - nothing seems to have any effect.

First thing is you need to confirm if you have a slowness issue while browsing the site
Check the IIS logs and look for the time-taken field. If the time taken is more than 10 seconds then it is considered as a Slowness.
The slowness might be because of several reasons. It might be because of the Network or might be because something in your code might be causing it.
I suggest you to capture a Network trace using Netmon or WireShark in case if its a Network related.
If its not Network you can collect a Process dump using Debug diag 2 update 2 tool.
You can check the below link to collect the dumps and check them and try to find out if there is any slowness:
https://msdn.microsoft.com/en-us/library/ff420662.aspx