You have circled a special page alias in your example. These can be translated at Special:AdvancedTranslate by selecting the module 'special page aliases' (the first on the drop-down list). Do not put any spaces in the translations. If you want to separate two words, you could put an underscore '_' between the words.
When you have translated as many as you would like to translate, please put a message on support to say that there are new Chechen special page aliases to review. It will take a little while before these can be manually checked and exported. It will also take a while after that before the new version of the software is updated on Wikimedia projects.
I hope that I have understood the question correctly.
Yes, you understood correctly. I moved here a long time but they do not work in our wiki although many times it was updated.
Unfortunately, saving directly in the page MediaWiki:Sp-translate-data-SpecialPageAliases/ce doesn't work. Please go to Special:AdvancedTranslate, choose the language ce and the module 'special page aliases', click on 'Fetch' then copy the translations into the boxes on the right hand side. When all is done, put a note on support.