Screed on concrete - when is it possible?

Hello everyone!

I am currently renovating an old house - room by room one after the other. In the study, I had a wooden floor on joists, now everything is gutted. Current status in the room: At about 20 cm depth below the intended floor level, there was a rather patchy concrete carpet. Over this, I laid a construction foil as a vapor barrier (rising high at the edges). Into this 11 square meter area, I poured about 25 mixes of concrete and leveled it somewhat evenly. So far, so good. Now my questions:

1. Some spots have set nicely and firmly. Some spots are still (after 5 days) so "clayey" that I can draw a furrow with my fingernail. What does that mean? Is that a problem?

2. When can the further floor structure (construction foil, insulation boards, screed) be installed? The screed installer said today that it doesn’t matter if the concrete is still that fresh. He wants to install foil, insulation, and screed already in 2 days (i.e., 6 days after pouring the concrete). Is that possible or is that too early?

Thank you very much in advance for your answers!

For clarification: "Betonteppich" means that there was a patchwork carpet of concrete, which was apparently poured at different times. 25 mixes means that I made 25 mixes myself with the concrete mixer and transported them in with a wheelbarrow.