Does lifetime of tungsten incandescent lamp shorten by every turning on, directly connecting to electric grid, and how much?
The tungsten filament thins with use and it will tend to fail when switched on because the current surge causes mechanical stress. This gives the user the impression that the lamp would have lasted much longer were it not for the turn-on surge. 

The life of an incandescent bulb is strongly (exponentially) related to RMS voltage so even a small decrease in voltage results in much longer life. Unfortunately, the efficiency also drops with the voltage so you have a choice of getting more light per watt that is whiter or getting much less light that is redder and having longer bulb life. Consumer bulbs were designed to have a certain trade-off like 1500 hours average life. It's no problem making a bulb that will last 5000 hours, it just will be very inefficient and will use a lot more $$ in electricity to get the same amount of redder light.  

I don't think there is much evidence that soft-start materially prolongs the life of an incandescent bulb. Many years ago I did a feasibility study on prolonging lamp life in a high-reliability application and we concluded it was not worthwhile.

If you still have any incandescent bulbs, I suggest turning them off the moment they're no longer needed, even if you're just leaving the room for a few minutes.