I do not understand exactly what you mean by this. Could you elaborate a bit?

The way I thought about it: imagine a hemisphere around the receiver center point's normal. In the first configuration, the emitting surface would be close to the Zenith of this hemisphere. In the second configuration, the surface would be closer to the Azimuth and thus the cosinus factor would be different.

Is this what you mean?

Yes, that is correct. The incident beam would be smaller due to the cosine factor, hence irradiance decreases by a corresponding amount. That is not radiance, though, but irradiance.

Assuming the receiver is left and the emitter right in your images:

That was my assumption as well. Perhaps this was not the expected interpretation?