Is there such thing a fake Mac installer?

Any installer you download from a third party could contain malware. Only download apps from AppStore, or directly from the developer. (Adobe Flash Player is a a good example, with many phony downloads on the internet.)

Genuine macOS installers are available from the App store, and you can be 100% confident they are genuine.

While it is certainly possible you may find installers for specific versions of Mac OS outside of the App Store, on some website, these should be considered tainted and potentially unsafe. While its possible there may be some that are clean and fine, why take the risk. macOS is free from the App Store.

No reason to want to get them from anywhere but the Mac App store.

The_Old_Man wrote:

Does those fake installers actually install MacOS or they will not work and will install virus into your computer?

No way to know. They could install macOS, they could install macOS with something else embedded in it, like a trojan or a keylogger. They could just install virus. Point is there's no way to know what they'll do until your run them.

You may get lucky and get a real installer, but you may not and get just a virus. There's no way to guarantee what you get.

In other words installers from anywhere but the Mac App Store can be potentially anything. No way to know for sure if they are good or not.

Where did you download Sierra from? Was it a link in an Apple document? Did you just download an updater patch?

You'll need to explain exactly what you did. in full detail. Where did you download Sierra from?

The_Old_Man wrote:

Does those fake installers actually install MacOS or they will not work and will install virus into your computer?

Yes, no, maybe. Until you try, you won't know. And, given that bad things can happen if you do try, it's a bad idea. Don't use installers that come from anywhere but Apple and you won't need to worry about this.

There is fake everything somewhere in the world. That includes installers that claim to install macOS. Don't use them.

Yes, there is FAKE Mac installer and on your Apple laptop or Apple computer look at the top left corner where you see the Apple logo and click on it and a sub menu drops down 'About This Mac' the click on it then a window appears 'System report or software update OR always get it from the Apple App Store. Since, we are talking about FAKE another one is Adobe Flash Player that sometimes it pops up on your screen. DO NOT DOWNLOAD IT BECAUSE IT IS A VIRUS. Millions of Apple computers were infected with this virus. On my free Apple class that I did the correct way is to go to Adobe.com and click on 'Flash Player' or go to your Application Folder and look for the icon Flash Player. Always go to the Apple App store. OR why don't your register for a FREE Apple class on a subject you like to learn from.

Not if you get it from the App Store.

but I don't know if the installer I got a fake one or not

The only legal ones are on the App Store. If you got it somewhere else you need to consider your Mac compromised.

In today's world you have a lot of FAKES on the internet. Always go to the Apple App Store. Example, when watching a video for example you see in small letters update flash player it is a Virus and some Apple user click on it then they received the virus. I learn from my Apple class that you always go to Adobe.com and click on flash player OR with the newer computer you might have it in your Application Folder or not. Click on it and it will tell if you need to update it or not OR it automatic update it for you.

OR on the top left corner next to the Apple logo click on it and a sub menu drop downward and look for about for this Mac then click on it and a window drops down. System reports or software update.

Hold Command and R keys on startup.

About macOS Recovery - Apple Support

Also if I download something from App Store, does it show on downloads folder?

No, it doesn't show up in Downloads. It goes straight into /Applications.

Also when I upgraded to High Sierra, does it keep all the downloaded files in the older versions?

Not the OS files, but other Apps, yes.

FWIW, if you used the patcher to allow High Sierra to run on unsupported Macs it does come from Apple servers.

Also for some reason when tried to press Command+R, my Mac went to Internet Recovery Mode and go back to Recovery HD of 10.7.5 instead of High Sierra. I think my Mac has been corrupted.

If it goes directly to Internet Recovery instead of normal Recovery, your Recovery partition is corrupt.

A reinstall from Internet Recovery will install the OS that shipped on the Mac, or the earliest available OS after that.

Apple has added some Options, though, that allow you to install the current OS. Given that, my guess is the fact that it could not find a valid Recovery partition, it reverted to the shipping OS instead of the current OS.

There used to be a Recovery HD disk. Now there isn’t on my screen.

The Recovery partition is not shown if the drive is formatted with CoreStorage or APFS.

However, it does sound like something is wrong. I would use Internet Recovery to run First Aid on the drive, then erase it and install the shipping OS. Then, Upgrade to the OS you wish to use. It may be that there is something wrong with the drive.