Please read again mu question and your answer from sept 26th. I didn't scroll to 8-10 and made a video to proof that. Please watch. I know only 2 reasons when playhead is on the beginning and piano roll shows later of timeline. The zoom slider is more on the right of its position and the region is activated in the middle of timeline (then piano roll shows it but the playhead is still in the beginning). But here are no these 2 reasons, I even scrolled to the beginning and it jumped still to the middle. What is wrong, any ideas.. ? https://youtu.be/YXuEkWZGjWY

The Catch button is supposed to make sure that you always see the part of the timeline where the playback cursor currently is. As long as the Catch button in the Piano Roll is on, whenever I placed the playback cursor at a particular bar the Piano Roll is centered at that bar. The only way I could get the playback cursor to be at bar 1 and the Piano Roll to be centered at bar 9 [as in your video] was to place the playback cursor at bar 9, turn off the Catch button, and move the playback cursor by hand to bar 1. But then when I turned Catch back on [as it is in your video] the Piano Roll jumped to bar 1, as expected. And even that worked inconsistently. So I don't know why it's doing what it's doing in your video -- I can't duplicate that here. GB occasionally has little bugs & behaviors that work inconsistently -- maybe this is just another one. I would just reposition the Piano Roll by hand when necessary and not worry about it too much.. Btw, if you want to revisit a question or discussion, please re-ask the question, or at least copy the relevant text into the new post..

Now I do realize why it happens. I checked the zoom slider ( on piano roll right at top ) and it is on the right position (makes larger the piano roll area). I changed track and slider jumped to the left and thus also bars were seen since first one as should be.. But you see, the notes are now so small on the piano roll after dragging slider from right to left.. Is that size of notes OK (if I have more regions on the track) ? But the thing is, I myself don't remember dragging the slider to the right. Does the zoom slider moves itself to right position... ? If yes, why and when then?

A video to the previous post https://youtu.be/vczN3HX6Fto

Yes, of course when you zoom out the notes will look smaller, to fit more bars in the available space -- this is normal. Apparently the Piano Roll zoom setting is independent for Software Instrument tracks and Audio tracks.

OK. Zoom on shows 8-10 and out shows from beginning + all other bars. But how can I zoom on the bars I'd want to? As zoom slider is on the right and it shows 8-10 for me occasionally. How can I see only, for example, bars 1-3, 4-7? I mean, how to zoom on particular part of bars which I need to?

Zoom does not locate to the bars you want -- it just zooms the display in or out around the current location of the playback cursor. And it doesn't always do that consistently anyway. In theory you would locate to the bar you want to see centered in the Piano Roll and then zoom -- in practice it's not always that consistent, so sometimes you may just have to locate to the desired bar[s] by hand. Logic has a feature that lets you zoom in to a particular area -- GarageBand does not have that feature. The zoom feature is not really related to this thread's topic [Regions] -- please start a new thread for a new topic..

I enclose you a video where is seen bright vocal's regions. But you can see, each of them has different number: 2.1, 12, 18, 19. What numbers are they? Each region has different voice, I understand, they are recorded in different keys.. ? But do the numbers are related to the keys.. ? I mean, any key has its number? If yes, where is a list of the keys and them related numbers? Because you can see there are not numbers from the beginning like 1,2 etc or between 12-18. These are the only regions I have recorded as much as I remember, I hadn't the regions 1, 2, etc at all. What numbers are they and why are they not in numerical order... ? https://youtu.be/-lc4KgMJNU0

The numbers have nothing to do with keys. GarageBand numbers or renumbers Audio Regions when you record, cut, or copy an Audio Region. The initial Region numbers seem to be assigned in the order the Audio Regions are recorded. New Region numbers are also created when a Region is edited [cut or copied] to create additional Regions, and these seem to be assigned in the order the new Regions are created, not in the order in which they were recorded or the order in which they occur in the song. So if you cut an Audio Region named Vocal#01 in half the resulting two Regions would be renumbered Vocal#01.1 and Vocal#01.2, or if you copy a Region named Guitar#03 the copy would be named Guitar#03.1. The numbering seems to only happen with Audio Regions when the name of the Region ends in a number already, like Vocal#02, for example.