A little grim, but I believe the answer is:
Older than history, as young as today, / I was here before you, and I'm here to stay.
People have been killing each other forever, and will likely continue doing so for a while yet.
My fathers were high, my mother had might
Murders are committed by the high and mighty.
I'm beloved of nobles, but never by right.
Nothing nobility likes more than a good old fashioned bit of murder (but that doesn't make it right).
Conceived in the garden, I walk in all weather / then disappear all black in a flutter of feather.
A murder of crows.
I dally with dahlias, I rib with the rose,
References to The Black Dahlia murder, and to serial killer Rose West.
I enter the forest surrounded by does.
Murderers often dump their victims (John/Jane Does) in forests.
I'm awarded degrees, yet not educated, / they judge me as worst among the related.
Generally considered the worst crime, and is graded in degrees (first/second degree murder, etc).
You always see me but hope we don't meet
Seen on the news/movies/etc.
I never respect you, but if you scream, I will bleed.
From the idiom, to scream bloody murder.
I'll arrive in a glass, or I'll arrive in a wave / and then my sad ballads will emerge from the cave.
Reference to musician Nick Cave, who has an album called Murder Ballads.