I would like to get less latencies by vocal recordings and decided to switch to ASIO4All driver.
But when I set it in the Preferences, I get only one Input device - Line Input. No Mic input. When I switch back to MME 32 bit driver I get Realtec Mic Input.
Does it mean that my in-build Realtec sound card is not working with ASIO driver?
 
PS. I do not know how, but after some switching of the drivers I have got a Micro Input for my ASIO driver (I didn"t delete the above, because I don"t know the secret). It says now, that the effective latency is 11,6 Msec. Is it OK, so I would not need to drag the vocal clip any time backwards to fit the music? Is it a way to get 0 latency? Sorry, if my questions sound stupid... :)

PC sound cards have poor latency and thus don't make very good recording devices.  Best option is to get a USB connected recording interface unit.  Even the relatively inexpensive ($150) units will get you in the 4 to 6 Msec latency range. 
 
Here is one example:
https://www.sweetwater.co..ore/detail/Scarlet2i2G2

Hi. I can almost certainly say that your Realtec soundcard does not support ASIO.
ASIO4ALL is a WDM wrapper to let your MME/WDM card see it as ASIO.
Some people report great performance using ASIO4ALL, but it is a tool for people not having access to native ASIO drivers from their manufacturers.
Hope it helps.
All the best.

This is an example of an $85 entry level USB audio device that will let you do proper recording on your PC.  The manufacturer provides ASIO drivers specific to this unit, so you can disable your built-in RealTek audio and use this instead.
 
It has a mic preamp and an instrument input.
 
https://www.amazon.com/Focusrite-Scarlett-Audio-Interface-Tools/dp/B01E6T56CM
 

yeah, asio4all is the best you'll get with the onboard realtek

abacab
This is an example of an $85 entry level USB audio device that will let you do proper recording on your PC.  The manufacturer provides ASIO drivers specific to this unit, so you can disable your built-in RealTek audio and use this instead.
 
It has a mic preamp and an instrument input.
 
https://www.amazon.com/Focusrite-Scarlett-Audio-Interface-Tools/dp/B01E6T56CM
 

I just got this to use with my laptop, and the latency / performance is significant compared to WASAPI or ASIO4ALL on my laptop.
Well worth it.