Could you say the pool is behind the house instead of beyond the house?
That would be "Bassenget er bak huset", which has a different meaning.
The plural "-er" is a 'eh/shortened ah' and a tapped 'r' (to me it sounds like a soft d). Forvo doesn't have "bassenger" yet, but other words ending in "-enger" are "trenger" (needs) [http://forvo.com/word/trenger/#no] and "senger" (beds) [http://forvo.com/word/senger/#no]. Whenever "-et" is added for a 'definite neuter', the 't' is silent, so the word ends in an 'eh/shortened ah' sound. An example is "huset" (the house) [http://forvo.com/word/huset/#no].
Not necessarily. It would be if you were standing in front of the house, but if you were standing in the back yard, it would mean in front of the house.
More likely, you'd use this if you were giving instructions to find the public pool, for example. "Beyond" is the best translation.
Is bortenfor used very commonly in Norwegian? Because very rarely do you hear someone say "something is beyond the house"
"Beyond the house" does not necessarily mean inside the same property. It could mean that you have to go beyond the house (past the house) to get to a specific pool. Not a phrase we use very often. "Behind the house" would most likely mean that the pool is in the backyard, right behind the house, within the same property.
"Beyond" implies that the pool is on the other side of the house (from where you are standing). It could even be a public pool that is located on the other side of the house - if you walk in the direction of the house, you will find the pool as you go around the house.