OpenGeek, that’s right!
In my.ini was set (by default) ’latin1’
It turns out that there are quite topics written on it with settings for connecting to DB.
The problem comes, from one side – the usage of hosting services, that don’t allow configuring the settings of MySQL, and on the other hand - uncertainty about the methods of connecting to DB. (How nice would be if MySQL used only UTF and no collations

)
I think, it would be a good idea, while installing MODx in the section concerning the connection to DB – under the select bar, to be written the following:
"If you are sure, that character and collation of the server and database are the same, then use SET CHARACTER SET. Otherwise, use the SET NAMES. For more details !
Would be good also to discuss whether it is not better MODx to use only UTF8 - hardcore set. This is a kind of extreme proposal, but it solves "the problem with character set" once and for all
Best Regards,
Lyubomir