I'm not sure the name
of an application should be translated. Some examples you show have the description of the application not translated, which I think it should.
Except for the last picture of I think the mintMenu settings, none of these translations are in the Linux Mint domain. Translations of application descriptions for example are part of each individual application, coming from the Ubuntu package base. Other parts may be from the MATE desktop.
Linux Mint Bulgarian translations are here, with indeed many not 100%: https://translations.launchpad.net/linu ... t/+lang/bg
(mintmenu is the one from your example, just needing 6 translations!)
Ubuntu Bulgarian translations are here, with indeed many not 100%: https://translations.launchpad.net/ubun ... y/+lang/bg
MATE desktop Bulgarian translations are here, with indeed some not 100%: https://www.transifex.com/projects/p/MATE/language/bg/
So what are you going to do about it?
Translations are community driven, as you will understand there's no way any project will have native speakers of all the world's languages... For Linux Mint and Ubuntu you would need to set up a Launchpad account, apply to join the particular translation team (see the pages linked to for details), and then you can start translating. Probably best to join the Ubuntu Bulgarian translation team first, find out how they work, and take it from there.
I've previously done some Dutch translations for Linux Mint. No special training required, you just need to understand the English and be able to translate that to your language. In many cases suggestions will be made for you from similar English texts that have already been translated to Bulgarian on other projects. Don't translate before you are a member of the team though, as in that case what you write is added as a suggestion and still a member of the team will have to pick that suggestion--instead of what you write being taken as the translation. You can also of course improve existing translations.