Phonology: How to classify /l/ and /r/

I have come up with a phonology-related problem. I do not quite know how
to classify /l/ and /r/. Different textbooks give them different labels
and also group them with different other sounds. I realize that this is
probably somewhat language specific, but there must be some underlying
logic that I fail to understand.

To begin with, why is it so common that the two sounds are only a single
phoneme in many languages? They sound very different to me.

How common is it to have more than two phonemically distinctive r/l
sounds?

What other sounds could/should be grouped with them, and why?

I am working on a phonology with four different consonant classes:
Fricatives, plosives, nasals and a fourth group including /r/, /l/, /w/
and possibly /j/. Would that be a good idea? If so, what should it be
called?

  /Fredrik

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