Relative clause and Participle

'Father bought a BMW' is the most natural way to express this, unless you want to contrast with some other mode of transport produced by BMW, such as in

'Father bought a BMW car (, and not a BMW moto).'

The other expressions are fine, except

The lying apples are on the table

sounds funny because my first reaction to this sentence is that you are saying that the apples are liars, because 'lying' is the ing form of 'to lie', which means both to recline and to tell a lie (fib, untruth). To avoid this, stick with 'the apples are lying on the table'.