How added MP3 files are managed in iTunes?

Beta,

If you add an MP3 to your library, you have a local copy. If you have subscribed to iTunes Match, iTunes will either match the file to one in the store, or else (subject to certain restrictions) will upload a copy of yours.

When a file is added, iTunes analyzes the volume level and creates a "volume" level tag that is visible on the File tab of Song Info. That is what it uses for Sound Check. Note that it functions quite differently than MP3Gain, as the latter actually modifies the audio level of the file.

Thank you for your reply.

I don't have iTunes Match. So, if my understanding is correct, then if I add my MP3 to library, that same file is uploaded to Apple Music and the same file is then available in all my devices (iPhone, Watch, iPad), right?

Yes, if you have an Apple Music subscription, a copy will be available in your iCloud library. See details here:

https://support.apple.com/en-us/HT204926

Regarding normalizing volume - if I add my MP3, where is already created tag about volume, is that tag ignored and iTunes creates it's own, or it is accepted and used by it?

Regardless of what processing has happened to the file previously, iTunes will analyze it and add its own "volume" level tag. If the previous program actually modified the volume of the audio, that will of course carry into iTunes. Either way, you should get reasonably normalized playback if you turn on SoundCheck.