Player rating for tournaments across all installments of Heroes.

We are talking about how to calculate the rating across ALL parts of Heroes.

I already said that this is not possible! only within the framework of some tournament. A good example: ВК where it is possible. Otherwise, it turns out like "a 100-meter race and a 400-meter hurdles!"
And instead, I suggest introducing a purely informational rating that shows the strength of players with the greatest accuracy, but according to which you cannot compare and choose winners! It is described here.

I am also against aging, because a player who has played one tournament may be pushed from his place in the second, because his rating has not increased, while those who have played – their ratings have grown.

That's right! And I’m saying the same thing!

The rating should be calculated after each stage, and not once a year (because we will find out the total number of participants only after the last tournament).

We will be able to calculate the final rating only at the end. After each stage, you can give an approximate rating (for information)

Both the time taken and the position occupied should be taken into account, as this would be much more objective. An oscillator is the best solution.

I completely agree with you.