Hello.

Can I install 1c:enterprise (nonserver version)  + web server extensions and 5-lic pack on this computer (lets call it server) and use it via http without installing licenses on "clients" computers.
In this particular scenario I could run Designer just fr om the computer wh ere 1c:enterprise (server) was installed? Will the licenses be provided by web server?

The short answer is yes, if you use web clients.

Licenses are registered for a particular computer, where they were obtained to. To share them over the network, you need a license server and licenses installed on that server. But in your case, when you use web clients only, you need the web server to have an access to licenses. The same situation will be for terminal server: all clients physically work on the same computer where licenses are placed.