Hi.
You can verify this for yourself with some CPU and GPU monitor.
In theory not for Cycles. But Eevee uses more vRAM the larger the resolution output.
Compositing nodes can also use more memory the larger the image resolution.
Edit:
There is a clear exception to what I said about Cycles, when you use procedural maps and especially with adaptive subdivisions. You read what @Lumpengnom has been saying.