Can you let the water run directly open out of the downpipe with it?
Maybe you could, but I wouldn’t recommend it. You’re introducing all the water close to your foundations, and with clayey soil, it will hardly infiltrate well. With permeable paving, it’s simply about the driveway not being sealed, so rain can still infiltrate there.
Is it really that simple? How do you get the water from the roof into it then? If it infiltrates slower than it flows off, won’t it back up in the downpipe again?
You would lay a pipe. The hole would of course have to be big enough so that water doesn’t constantly stand in the pipe. I haven’t done something like that myself (we are required to have a cistern) but I have read about it in gardening books. An alternative would simply be to set up rain barrels; that also collects normal rain without a cistern.
We don’t yet know what kind of soil it is (we were always told that a soil report is only done once the building permit is granted).
Call the municipality; they should also have a soil report from the site development. That is sufficient for the assessment. If you’re building with a basement, I would definitely find out if you have to build with a waterproof concrete structure (“white tank”) in case of clayey soil. If so, you can pretty much forget about infiltration on your property.