Looks like clutter, especially as many entries seem to be redundant (Example/Beispiel).
I would suggest to use only English names.

For german texts we need the german ones, that's why I included them. I was thinking about a way to present only german ones if german is selected as language in the options and so on. But I don't know how to do so. I have seen that there is alreay "executable" code. Can you tell how to do menu depending on language?

no, the entries language independent (the menu texts can be translated)
Usually the language change is done via tex, see caption.

I see that some words in the menu change on language change. Where can I see which words are those? What is caption? If f. ex. I use env Example the result in the document is Example, it is not translated to Beispiel, what I need. Can I change the code to resolve this? Sorry for all the questions.

I was talking about \caption{}, I have not looked into the tex code. I assume babel is involved.

I would expect, that you want to use env completion for this problem.
E.g Beispiel ctrl+alt+space
I am not convinced that it needs to be in the menu.

so we forgett about german, I will remove those envs. Should I remove the menu "math definitions" at all (as it was bevore) or keep the english ones? And I would keep all other changes, right?

you can keep the english theorems and the rest of the changes

@sunderme How are translations affected by my changes? For ex. here (file texstudio_de.ts and other translation files):

<message>
    <location filename="../src/additionaltranslations.cpp" line="25"/>
    <source>Math Equations</source>
    <translation>Gleichungen</translation>
</message>

I changed Equations to &amp;Equations in uiconfig.xml, and I assume that <source> will be updated automatically in the part above. But I have to change Gleichungen in say &amp;Gleichungen. Can I do this immediately or do I have to wait until update is done?

translations can be done on transifex (see texstudio.org) after I upload the source.

thanks