I've read all of manuals, faqs and so on - it doesn't work.

I've got preconfigured LAMP installation on my local machine. My local hosts resides on the mounted via subst command drive Z in folders Z:\home\test1.local, Z:\home\test2.local and so on. Each of those local sites have directory www which works as root directories. And all of those sites mapped in windows/system32/drivers/etc/hosts file, so they respond on http://mywebserver and http://myweb2server. And it works great when I'm pointing my browser on this domains.

Now I want to map this domains in PhpED accordingly to my local projects. I go to the project properties, set Root directory as Z:\home\test1.local, Run mode as 3rd party web server, Root URL as blank and Remote dir as Z:\home\test1.local. Then I go to the Mapping tab and add there one more record with Remote and Local dirs set as Z:\home\test1.local\www and URL as http://mywebserver.

Then, trying to Run project I've got an error message saying "Can't run 'Z:\home\test1.local\www\index.php' file. make sure that 'Remote root directory' and 'Root URL' are correct in the project settings. For more details blah-blah-blah".

What am I doing wrong? My PhpED version is 5.0 buid 5019.

Have you tried setting the root URL?

What Stryks says is correct, you cannot leave the root url blank, it has to be set to http://mywebserver in your example. That should work normally.
Small hint btw: Leave the "Default file to run" empty, that way it will use the file currently active in your IDE to run.

if you run your web under Linux, remote path will be something like /var/www/blah blah blah/, and would never start with Z:\
It's Remote path - e.g. on the remote file system, it's how server sees the files.