Keşke and bir are often used in wishes just like only in English.

         Senin adını bir bilsem.

         Sen bir sussan.

         Keşke hayat gözlerimin gördüğünü gibi olsa.

         Keşke görmeseydim seni.

They are not necessary to make the point, are they? Are they interchangeable (for instance in the above examples)? Does any one of them prefer negative sentences?

They are not interchangeable (at least for your examples). They change the meaning somehow. They can be used with affirmative/negative sentenes (no restriction).

That´s too bad. So often it seems that bir has fallen to the sentence from the sky. Not in wishes only. No way for a learner to get it right.

Yes "bir" can be used as an adverb too, meaning only, (for) once etc.

I will have to make some observations about it. Thank you, si++.