At least in the U.S., they deliberately adjust the speed of the generators so that the frequency averages 60Hz over time. They may lose a few cycles during periods of high demand, but they make up for it later. The clocks in my house that are driven off line voltage are very, very accurate over the long term; I only need to adjust them when daylight time changes. (This is much more accurate than my wristwatch or my car's clock, which need frequent adjustment.) Since I don't have to set my alarm clock or time my cooking with split-second precision, this works out well.
They do. Most likely the frequency is adjusted during night hours (when there is less fluctuation) such that the average comes to 50 Hz (or 60 Hz in the US). (See [1].)
They do. Over a day, they end up getting the clock back to the proper time.
Keep in mind that in a complex power system (any modern system in an industrial company) that there are multiple interconnected power-generating elements. The difference between a motor and a generator is simply a function of the relative phase. that is to say, if there are two interconnected generators operating, the one that is slower will draw power from the other proportional to the relative phase angle between the two.
The story told is oversimplified, as they are only noting one particular type of event (turning on kettles at the end of a TV program), whereas in any complex interconnected power system, there are events that are much less predictable.
I suspect that in lots of systems that it is much less manual than the video shown.
Before they started making electric organs, Laurence Hammond's company made luxury AC clocks. The problem was that they didn't keep very good time because of fluctuations in the grid frequency. The story goes that he solved this problem by making gifts of his clocks to the executives of all the power companies in the areas he was selling in to, and within a few months, all his clocks were keeping perfect time.
Frequency as in the alternating current alternates direction fifty times a second (or sixty in some countries), not as in power usage is consistent throughout the day. This didn't change the frequency. (Disclaimer: I haven't finished watching the video yet.)
