Russian nuclear doctrine suggests they would only use those weapons if Moscow was under attack doesn‘t it? Existential threat to Russia, its been mentioned a few times that Moscow IS Russia.
Yes. Though, as I understand it, the G7 have only given permission for the Ukraine to enter border territories (Kursk, Bryansk, Belgorod). i don't think they have any intention of going to Moscow. It is likely designed to do several things. Ferment discontent, be diversionary and draw Russian forces from the south, create a bargaining chip, undermine the Russian propoganda narrative. Whether or not it works out that way, who can tell?
I might add that China has told Russia that using nuclear weapons is a no go.