As far as I can see, there's not a specific rule about whether you put the house name on the building or on the entrances. But it shouldn't need to be in both places because that creates clutter. 
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For the playground -- yes, personally I would just add a barrier=fence tag to the playground. Sometimes though, that's not correct -- for example, if part of the perimeter is a fence and part is a hedge. In that case, the playground, fence and hedge would need to be separate ways. But those ways can share nodes 