Just copy image from somewhere to clipboard and try to paste it with menu Edit->Paste. I think this should work like in other graphics programs. Reproducible: Always
This option exists already. Go to Edit > Paste Into New Image. We might be able to modify Edit > Paste, but it is probably ok with the existing way.
No I dont think so because if one click on menu entry and nothing happens is not good. Could you open that window when press Edit -> Paste