There are a lot of questions within your question. I attempted to break them down for you.
Remember that Fenton is actually Adam. When he introduces himself as Fenton at the Police Station, he is well aware that the FBI will be searching for Fenton, NOT Adam after agent Doyle is found dead.
Since Adam introduced himself as Fenton at the FBI office, he knows
that the investigation of Doyle's disappearance will center on Fenton.
The authorities will discover that Fenton was the God's Hand serial
killer and conclude that Doyle became one of his victims.
Having arrived at the rose garden with Doyle, Meiks confesses that he
is Adam and that he has destroyed Fenton, who grew up to become the
God's Hand serial killer, as a demon.
Adam was aware that not only could security cameras not record his image, but nobody could remember his face, even seeing him in person.
Those who saw Meiks at the FBI office, including Agent Griffin Hull,
inexplicably remember nothing about "Fenton" Meiks' appearance.
Surveillance videotapes all have a distortion when played that
obscures Meiks' face. The investigation then proceeds as Adam had
After Adam reveals who he actually is to agent Doyle, he informs agent Doyle that he is a demon and that he is on the list to be destroyed.
When he touches Doyle, a new vision reveals that Doyle had murdered
his own mother. Meiks tells a dazed Doyle that Doyle's name was given
to him on the list of demons to be destroyed.
Adam kills his victims in this manner because that is the original "vision" that his father had when visited by the angel. All victims must be buried in the Rose Garden.
The father's modus operandi is to wait for the angel to give him a
list of names of those who must be destroyed. He then abducts an
individual from the list, takes them to the family home and, with his
sons present, touches them, which, he says, grants him a vision of the
crimes the demon has committed. He then finishes the victim with an ax
and buries the body in the rose garden.
Although Adam does not know the actual sins that the "demons" committed, he does receive their names in his "visions".
You had stated that Adam is "gifted". The main thing to remember is that Adam is "protected" by God. He is above the law and cannot be identified because of God's help and protection. It would not matter if the FBI agent called somebody else.