Internet Sharing: restricted set of WiFi channels
Don't select a channel manually, let auto-select handle it for you.


  Unfortunately, all these channels are overcrowded by my neighbors (3 to 5 on each of these channels) and can't be used.


You're absolutely correct - at this moment.  This changes continually as traffic increases/decreases.  

How can I use my Mac to determine the optimal WiFi channel to use with my wireless router?

As people light up hot spots, turn on AirPlay, AirDrop, screen casting, etc. it all "lives" in the same 2.4 and 5GHz bandwidths.  Letting your Mac or WAP automatically detect and switch channels for you will ensure you get the cleanest channel at the time.


  Which program build this small list of channels?


That was created dynamically.  Those are the channels that have the "best" signals at that moment.  

Now, if bandwidth congestion and more than likely noise are causing connectivity issues, it's much better to get multiple WAPs (Wireless Access Points) with the transmit power reduced than to get one, crank up the power and shoehorn it into a particular channel.  Think of it like trying to setup  speakers for a party in a noisy environment.  It's better to have several speakers dialed to maybe a 4 or a 5 than to just have one speaker cranked up to 11 and then the knob subsequently broken off.

Additionally, getting a newer, modern WAP (you don't need a full blown router) will give you much better performance because you'll have the option of placing it higher up (like on a shelf or bookcase) where devices will have better line of sight to the antennae as opposed to the MacBook on a desk.