Is there a difference between shut down and sleep in case of the wealthware of Mac? I prefer shut down, as it takes less battery. So the reseller of Apple told me, no difference. But I read from internet, the Macs are assumed to use sleep, because the computer will make a lot of useful during the sleep. Is it true? Or not? If I mainly use shut down, is it bad for Mac?

The Mac OS does system maintenance stuff in the background overnight [in the wee hours like around 2-6am or so] that helps to keep it running efficiently -- if you put it to Sleep it will still do those things, but if you Shut Down overnight it will have to do them when you power it back up, which may slow things down for a while at first. BUT.. If you run music software [like GB or other DAWs] on a Mac, DAWs usually advise you NOT to use Sleep [disable all Sleep options in Apple menu > System Preferences] because it can cause problems with music/DAW software. I disable Sleep and usually leave my Mac [an iMac] on overnight, and shut it down when I go out. However if the Mac is a laptop there are usually separate settings in System Preferences for Sleep for when it's running off the battery or when it's plugged into a wall power outlet. In that case I guess you could disable Sleep when the computer is wall-powered [and run it from wall-power when using DAW software], but you might have to have Sleep enabled when you're out and about and it's running off the battery to conserve battery power -- I'm not sure what DAW makers recommend in that regard..

What means computer is wall-powered? Feeding a battery.. ?

You plug the power cable/adaptor [that came with your computer] into a wall outlet, like any other electrical appliance.

I opened Apple menu system preferences, but there was not a sleep option. To disable sleep options. Maybe they are already disabled, as my Mac sleeps only when I tap on sleep (from menu sleep restart shut down). Where is a sleep in the system preferences?

Sleep Preferences are found in the Energy Saver panel in System Preferences.

What is sleep exactly? If I don't shut down and just close the cover, then battery quickly goes empty. If I choose before closing the cover from apple menu sleep, the battery gets empty slowly. On my mac under energy saver is active "put hard disk to sleep when possible". What that sentence means? As without extra sleep order the mac doesn't put hard disk to sleep itself? Because battery goes empty without order, but by that active sentence it shouldn't.

Just keep the Mac plugged into the wall AC when you're home or if you're letting it sleep overnight -- then you won't have to worry about the battery running down. https://support.apple.com/en-bw/guide/mac-help/mh10330/10.15/mac/10.15

How often can I put my Mac to sleep per day? Is it OK to do it 7 times with short intervals? For example, I think to keep it in sleep some hours, but just after 10-30 minutes I still need to use it and awake it again...

Here are Apple help documents on Sleep: https://support.apple.com/en-hk/guide/mac-help/mh35848/10.15/mac/10.15 https://support.apple.com/en-hk/guide/mac-help/mchle41a6ccd/10.15/mac/10.15 https://support.apple.com/en-hk/guide/mac-help/mchlp1373/10.15/mac/10.15 https://support.apple.com/en-hk/guide/mac-help/mh40773/10.15/mac/10.15