Android system recovery from Windows I have the cheap Android tablet. During my experiments, I had rooted it and removed application folder. Now I can't turn on my tablet it is loading forever.

I have read about ways to load new ROM on my phone. Most of them start from uploading some apps on phone. I can't do it.

Also, I tried adb tool. But command: adb devices don't see my device.

Is it possible to recover Android system in some if Android OS isn't started and adb tool doesn't see the device?
Deleting system folders can brick your device. That's what happened. Some files are part of the booting process and since they are not present the system can't go further. To be able to boot normally again, you'll need to flash the firmware/ROM for this model. 

ADB can't find the phone on this state because android needs to completely boot for USB Debugging to be operational.

As this phone is a Mediatek device, you'll need SP Flashtool as the flasher software and flashing files need contain a scatter file which is a sort of phone internal chip memory "map".  Also you need MTK drivers to allow the phone be detected. 

You can find thousands of video tutorials on how to flash a Mediatek device using SP Flashtool. Flash files can be found on Needrom