Is there any list of formulas for quick counting navigational parameters of the flight, if navigational computer is malfunctioned.
For example, I need to recalculate how long can I fly, if the wind is changed.
There is no short list but almost all the navigation information you could ever want can be found in this handbook published by the FAA. If you are worried about your nav computer failing you can always get an E6B which is about as close to failure proof as you can get. An E6B will expedite most most nav related calculations in the air (like headwind component). My E6B has some common nav calculations written on the back of it actually.
This is not exactly a "rule of thumb" site, but a friend has put together aviation formulas for the last several decades, available at: http://www.edwilliams.org/avform.htm
Rules of thumb for navigation are different, and while I have probably 40 books on navigation alone, the rules of thumb are distributed among them. As technology changes, the rules also morph. For example, rules specific to NDB and ADF navigation are almost obsolete these days, and have low relevance to most pilots.
Meanwhile you will find a collection of formulas in the above reference. And the FAA publication @Dave mentioned will be an excellent general read.