Yes, a murderer can be forgiven. King David committed pre-meditated murder and adultery. He sincerely and agonizingly repented of his sin and was forgiven. Indeed, in spite of this major lapse, he is described as "a man after God's own heart."
Likewise, Manasseh, King of Judah, committed mass murder and idolatry but later came to his senses and repented and God forgave him.
Even Judas would have been forgiven had he repented and sought forgiveness. His great sin, besides his betrayal of the Son of God, was to think that God's mercy was not large enough to include him. It would have been had he sought it.
I hope you have found this helpful.