Fallacies involved in arguing for God or mythological characters

"Person 1: Just like how the PhD thesis of Stephen Hawking is evidence that he was intelligent, so too, in a similar way, the universe is evidence that whatever the cause behind it is intelligent and extremely powerful, and that's what we call God."

This would be a non sequitur fallacy because the premise of Stephen Hawkins PHD does not have anything to do with the universe being intelligently created or not by a God. The premise and conclusion are not related at all and does not follow. Therefore its a non sequitur. It also might be a false equivalence fallacy trying to equate Stephen Hawking's phD and intelligent design. Its also ironic that the argument argues that Stephen Hawking is intelligent therefore God when Stephen Hawking said he believed there is no God. 

"Person 2: Of course God is the Holy Trinity! Don't you see the triunity of time (past, present and future) and dimensions? That clearly demonstrates the nature of God!"

This one is such a mess its hard to even analyze. Maybe an argument by gibberish might be in order. "Of course God is the Holy Trinity" is not evidence or a demonstration, its perhaps a kind of circular reasoning fallacy like a complex question fallacy or a begging the question fallacy. "Dont you see" is probably a fantasy projection of some sorts. 

Person 1 is a faulty induction, or fallacy of composition that posits that something is true of the whole because it is true of the part.

As Dr. Bo writes:

Description: Inferring that something is true of the whole from the fact that it is true of some part of the whole.  This is the opposite of the fallacy of division.

Logical Form:

A is part of B.

A has property X.

Therefore, B has property X.

All creatures are God’s creation

My dog is the stupidest animal in creation.

Therefore, God must be just as imbecilic.