I have a simple wordpress site with phpMyAdmin panel for creating a database. The database which I have to use is so called native xml db eXist-DB and I don't know how to connect it to my website or how to import it. Is there any software or may be plugin to do this?
You cannot use Phpmyadmin to connect to eXist. It's a completely different Technology than mySQL and mariaDB. Don't use eXist if you are beginner. You'd need to learn an absurdly complex technology stack that almost nobody else uses. (Read "Recent News" section how one Java/XML Expert wrestled with eXist in 2010. I doubt it has become much easier).
If you must:
Read the docs on http://exist-db.org/. Download eXist. Ask a Java Programmer how to setup the tooling infrastructure (JRE/JDK, Maven, Tomcat/Jetty.... whatever else) and connect to the database.
If your website is simple, maybe your legacy data stored in eXist is simple too. Just let an expert extract the data in a one-off task, and store the data as CSV file, perhaps. Then forget about eXist.