Nicely done for the first scene!
In my experience you have to set up lighting separately for eevee and cycles (or if you aim at cycles don’t focus too much on lighting detail while previewing in eevee). Or at the very least tweak it if you switch between rendering engines.
I think Cycles didn’t miss your light, it’s just that it’s more realistic (so for example no harsh shadows). The effect with area lights are much softer usually.
Noise in cycles is inherent to how path-traced rendering works. You can reduce the noise by increasing sample count, or using AI denoiser (or both). I have posted simple compositor setup here Lesson 13 - first render comparison. But you might also look up in google / youtube tutorials to learn more about it.
And welcome to the community!