I have a new software update Big Sur. Are the softwares also Sierra and Catalina? Do the new ones are releasing so quikly? As Catalina is quite new, I guess... I only have it few times - and I like it less than Sierra.

If you use music software you should never upgrade to a new version of the OS until it's been out for around 3-6 months. Currently many plug-ins and DAWs are not yet compatible with Big Sur, so if you've already upgraded to it you may run into problems if you have any 3rd-party plug-ins or music software other then GarageBand or Logic. If you haven't actually upgraded to Big Sur yet, don't -- stick with whatever you're currently running -- Mojave or Catalina -- for the next few months at least.

If I go to apple menu system preferences software update then I can read unable to check the updates make sure you are connected to the internet. But I am connected to the internet. Also, there were 3 updates, one is security and two safaris. I did security one, it told that restart is required, but mac didn't make a restart, and now all 3 updates are disappeared there to nowhere. Why?

Maybe the restart box was just a generic notification, and a restart wasn't really necessary for that particular update..? I suggest you manually shutdown/restart the computer, and then check if those updates are still available -- if not then I'd guess they were applied.. But I'd still be careful with those incremental updates, especially security updates -- I'd still avoid doing them until they've been out for a while and I'd checked on various forums for reports of issues with third-party applications & plug-ins.

Is there difference between shut down and restart? I have shut down mac multiple times, still "not connected to the internet" and not is seen all my 3 updates. Now I made restart and all 3 updates are here again..Why are you careful about security updates? Aren't they necessary? For protect the mac?

Shutdown physically powers down the computer and flushes the caches, which can get rid of any bad code or corrupted background operations -- it also runs diagnostics at startup that can detect and address some left-over issues. Restart doesn't do all that so it's less likely to solve some problems, which is why when you're having inexplicable issues you should always do a full shutdown, wait around 30 seconds, and then power up again. OS updates -- especially security updates -- can occasionally break third-party software [and even Apple software at times] -- it happens often enough that most audio/video people don't do ANY updates, no matter how minor, without waiting long enough [weeks/months] for reports of problems to surface on reliable user forums, and then doing their due diligence [research and an up-to-date bootable backup] before updating. If you want to take your chances and succumb to Apple's pushing to always stay current, then go ahead, but unless you maintain a current clone backup and know how to do a full restore, I would instead turn off automatic updates and follow the recording studio mantra -- "if it ain't broke, don't fix it".

OK, now I got it. If it ain't broke, don't fix it. I'll live with that. Thanks.

Well, I turned off automatic updates. Do all these turned off updates still will remain in anywhere, for anyhow.. ?

"Do all these turned off updates still will remain in anywhere, for anyhow.. ?" I don't really understand the question.. If you're asking if updates you've already done will stay updated, then yes.

No, I am asking, if I don't do updates, but I decide them do for example a year later, will these updates still anywhere are "waiting" for me? Or what happens to updates which are not updated? Is there a list of the non-updated ones ?