No - the 622 and 630 are the respective bead seat diameters, so if you get the bead of a 27in tyre seated on one side of a 700c rim, at the other side it'll be nearly a cm too far out.
(And yes, 29er rims/tyres are also ETRTO 622, so the same diameter rims as 700c and smaller than 27in ...)
Yes, 700C = ETRTO 622
No, an old English bike with 27" wheels means ETRTO 630, i.e. about 8mm larger diameter than 700C