> Try copying a number from Safari iOS into Google Hangouts Phone dialer. There's no paste option

The paste option is there, however it's very tricky to get it to appear. You have to hold your finger down over the space where the number appears, but sometimes you have to try it 5-10 times to get the paste option to actually appear. Before Google Voice shut off external integration and ruined it I had an app called Talkatone which worked with Google Voice, Hangouts has never been as good as that app.