Words for specific omnipotent qualities

Question

I'm writing a story about a powerful god with specific abilities, which are:

• he can hear everything, no matter how far, and he can read minds
• he always knows where someone is or who is nearby, but he can't see everything (he does have exceptional eye sight though)
• he is a "person" in that he is only one presence, he's not someone who is everywhere, can see everything and knows everything
• he can't make impossible things happen (he can't cure someone's blindness for example), but he is powerful in that he has immense physical strength, enough to destroy a planet if he wishes to

Obviously, I don't expect there to be a word that matches exactly those very specific points, but I hope there is a word for each point at least.

Answer 1

From Merriam-Webster:

godlike: resembling or having the qualities of God or a god

In taking on the full power of a sun, at the risk of his life, in order to forge a weapon to defeat Thanos, Thor displays his full godlike potential.

There's also superhuman, phenomenal, incredible, awesome, titanic, terrible...

You'd have to use it in a phrase: "godlike strength" "godlike hearing"

Answer 2

I think superhuman fit this question: TFD

1. Above or beyond the human; preternatural or supernatural.
2. Beyond ordinary or normal human ability, power, or experience

As in:

Advances in science, engineering and biotechnology will produce a superhuman in the near future. Scientific American Aug 2, 2018

Answer 3

This person could well be a demigod.

demigod
1 : a mythological being with more power than a mortal but less than a god
2 : a person so outstanding as to seem to approach the divine
the demigods of jazz

Answer 4

I suggest telepathic for the first three points you made. This adjective also avoids including "god" or "human" in it. I believe since you specifically referred to the character as a "god", using the word "godlike", "demigod", or "superhuman" would misvalue the character or unhelpful in description.

Here are some definitions of telepathy/telepathic:

• Google: supposedly capable of transmitting thoughts to other people and of knowing their thoughts; psychic.
• Merriam-Webster: communication from one mind to another by extrasensory means
• Dictionary.com: communication between minds by some means other than sensory perception.

I think you still have to explain your god character's ability to readers though. The word encapsulates the three points, in my opinion, but it is ambiguous enough that I don't think readers will know the abilities precisely.

As for the last point, "can't make impossible things happen", I can't make a proper suggestion. Superhuman strength suggested by lbf above might be your best bet for that ability.