How exactly do funnels work?

Could you elaborate on how the player's actions in the funnels are accounted for with specific examples?
On different days. Within one or many game sessions.

For example: we have a level with a generated map. And there are several events:
1. the player has selected a level to play and is watching information about it and the rewards for completing it (GUI level event).
2. Generation of the level has begun.
3. Generation of the level is successfully completed.
4. The player has successfully completed the level (with a parameter stating how many attempts he had to do it in)

Suppose the player came in, looked at the information about the level, but did not start the generation. Later same gamer from same device came in again, looked at the information again, started the level generation, this generation successfully completed and then he successfully passed (finish) the level.
Am I right to understand that (roughly speaking) it will look like two chains triggered events:
1. true
2. true, true, true, true (1 try) ?

 

Not sure what you mean by 1 and 2 and triggered events. What does your funnel step definitions look like? But to address your question, this likely would look like one user made it past these funnel steps once. No matter how many times a single user tries, it will only look like one success to us. I would recommend that you try it and see.