HELP

Very odd. Are you sure it disappeared? Maybe he got lost or the bed was destroyed and he spawned elsewhere?

It's hard to say. It depends how far he wandered from the default spawn point before building his house. Chances are it's within a few hundred meters radius of the spawn point.

You could try searching for the house. First find out what kind of biome he built his house in (was it grassy, a forest, a desert, mountains, etc). Here is link to example pictures of biomes.

Secondly you could conduct a search for his house. You need to keep track of where you are searching exactly (so you don't search the same location repeatedly or go around in circles). Press F3 to display debugging information about the game. From here you can get your X,Y,Z coordinates. Just pay attention to the X and Z. These are your location in the game world. Ignore Y, that is just your height.

Using your coordinates as a marker, systematically search an area in a 200 block radius of the default spawn. Do this by adding/subtracting 100 to/from both coordinates. For example, if the default spawn is X:50 Z:250 then you want to search everywhere between X:150 Z:350 and X:-50 Z:150.

When you're searching it may help to find some high ground or build some simple 1x1 towers around the place to get a birds eye view. Finding out what biome he was in will help a lot to eliminate searching unnecessary spots. Starving to death and dying during night time will slow you down some, but keeping track of your coordinates should help alleviate this (also try setting game difficulty to peaceful in the options screen).

Hope that helps, if you have any more questions feel free to ask. If you don't understand let me know and I'll make some pictures to illustrate my points