As-salamu alaykum Bandaar,
Verse 6:74 makes it absolutely clear that Prophet Abraham's biological father was Azar.
006:074 (part)
"And when Abraham said to his father (Arabic: abihi) Azar,"
This is primary evidence direct from the Quran. This is the starting point. No argument, narrative sourced outside the Quran (including Islamic secondary sources), interpretive lean can deny a clear verse of the Quran.
With regards as to why Prophet Abraham prayed to his father, verse 9:114 makes this clear.
009:114
"And the request of forgiveness of Abraham for his father was only because of a promise he had made to him. But when it became apparent to Abraham that his father was an enemy to Allah, he disassociated himself from him. Indeed was Abraham compassionate and patient."
I hope this helps, God willing
Regards,
Joseph