As far as which tire will fit which rim, the outside diameter of the tire is irrevelant, other than the issue of rim width/tire width, which is a whole 'nuther matter (fatter tires are generally wider tires, etc.). 29" mountain bike wheels are actually 700c rims with fat mountain bike knobbies on them, for example, and the outside diameter of the inflated tires will usually be in the close vicinity of 29," hence the name. But the bead seat diameter of the rim is exactly the same as a road rim designed for ultra-skinny 700c road tires. I've got a friend with a 29" mountain bike, she uses 29" x 2.2" knobby tires on the bike for off road riding, and 700 x 32c slick tires for road riding. Quite a difference in the outside diameter of the tires (at least 2" I'd say), but the same rims for both.

27" rims have a bead seat diameter of 630mm, 8mm larger bead seat diameter than 700c rims, which have a bead seat diameter of 622mm. If you have two tires with identical sidewall heights, and one is a 700c tire and the other a 27," then yes, the 27" will have a slightly larger outside diameter.

Inner tubes are interchangeable for the two sizes, as long as you take into account the width range. The tubes these days are usually marked 700c, but they're plenty stretchy enough to put on the slightly larger diameter 27" size without it making a difference-