Should a mobile game button (say 72x72 pixels round one) be created in these exact dimensions or create it in a larger resolution and export a low resolution file? I think working with a larger one is much easier. How do professionals do this?
The most professional way would be to make it in vector, so it is resolution independent. Then, export in any size you see fit.
You could try to do this is Photoshop as it has some vector tools that will scale when you change their size. If you have access to Illustrator or a similar vector editing program like Inkscape, that would be the superior option.
Having a vector (or very hi-res) source file ensures that you are able to export your assets at any desired size. For now, that button might just need to be 72 x 72 pixels, but what happens if it gets included in an ad banner 20 metres wide?