Since Minecraft on the Xbox 360 is not unlimited like the PC counterpart, will every level generated have every biome available?
If not, are there any types of biomes that will guaranteed be available no matter what the seed?
No, it's entirely luck of the draw. The world seed determines what is generated, just as if it were an infinite world, but then it's cut off at the boundaries.
I dont think every Biome can be on one Map on the Xbox 360 Version but there might be some update to make the world bigger Thus more room for building, Exploring, Mining and so on.
I'm pretty sure it can happen but it's a very low percent chance. If u get lucky enough it could happen - when you play Minecraft anything is possible so all biomes might be present in one world but nobody really knows so lets just wait and see.
Also one time I came so close I found 22 of 23 biomes - I guess that world didn't bring enough luck. so I tried so many times but remember in Minecraft any thing is possible.