Will a 32" tv fit into a 32" wide space?

Well, that depends on the TV. A TV picture measurement is corner to corner. So bottom left corner to top right corner is 32". The doesn't mean the TV is 32" across. But you also have to take into account the framing around the TV. The best way to figure it out is to measure the TV with a measuring tape. Also keep in mind that a flatscreen 32" TV is wider than a traditional 32" TV due to the 'widescreen' feature.

A "32 inch" TV has a screen that's 15.7 inches high and 27.9 inches wide, or about 28 inches. Allow an inch or so on each side and a typical set will be around 30 inches wide, maybe 31.

So yes, it would fit into a 32 inch wide horizontal opening by a small measure. Of bigger concern is the space at the top. Such sets give off a lot of heat in normal operation, and they must have a lot of open space above them to dissipate it. Putting a modern flatscreen in any cabinet with little or no room above the set is a mistake.

That depends on how wide the 32" TV is.

Screens are measured on the diagonal, but there could be all sorts of plastic and speakers on the sides of the screen that makes the TV cabinet wider than 32"