"in the UK victims of violent crime can be awarded a payment from the criminal in lots of cases"
Like in most places, I would imagine, but this payment does not let the criminal get away without a jail sentence. You get the punishment the law says you get for the crime, and on top of that, you pay for the damage, loss in earnings, etc that you have caused.
"in turkey..."
Don't get me started about the travesty that legal system has become in Turkey in recent years. In any case, it doesn't have diyya and I not think of a word that would be its equivalent in Turkish.
"is the emphasis in criminal law about what laws have been broken? who did it? and what does the offender deserve?"
I believe this is what all Western law is about, yes.
"or is it about who has been harmed? what are their needs? whose obligations are these?"
Where is law about any of that? I'm guessing that you didn't go about finding out exactly who was harmed by that man's death, but just gave the money to a family member. What about his best friend who maybe can't get over his death, the company he was working at where maybe he was a key man and they struggled after his death? Did he have a mistress who loved him? She needs a man to keep her warm at night and whose obligation is it to find her another man now?
"does diya mean they have escaped punishment or is it also not a punishment itself?"
Well, he escaped prison for life and is now out living his life while the man he killed is dead and buried, so yes, we can safely say that he has escaped punishment by buying it off.
"witnesses to crimes being bribed or intimidated not to appear in court"
There is something called forensic science these days, that has largely diminished the weight of unreliable eye witnesses.
Not that it's even relevant. This isn't about identification of the criminal, it is about what to do to him once he has been identified and found guilty. In a diyya system the suspect can also refuse responsibility and then you would still need eye witnesses, forensics etc.