I'm trying to share the master site with a created slave one, but there is a problem:
As I understand, slave site shares the whole files and DB completely, except, for example, templates folder (if I want have it different). But why then, after I created a slave in this way, I get new Joomla installation and no way to avoid it? I suppose that I should receive, in fact, the same site, but with a different "layer" as "templates" folder. Thanks in advance.

If you share the whole website, you should not receive the "Joomla Installer".
If you received the "Joomla Installer" this is the symptom that you want create a fresh slave site and not sharing the whole website.

When you create the JMS template rule, verify that you have the same table prefix in the rule and that you have enable the "share whole site" check box.

You can also get the same result if you are "replicating" a website that provide the same table prefix as the website that you want to replicate.

Eventually I've got the idea - I was leaving DB name and server fields blank thinking that component will take values from parent configuration file. When I filled server name, db name and prefix - everything began to work smoothly.

Thanks for your help!