Yahweh is the name of the Father whom Jesus referenced, but Elohim is plural and means "Gods".
Elohim isn’t the personal name of the Father; the tetragrammaton (YHWH) is.
Presumably Yahweh is included in this group, but then who are these other Gods? Who is the "us" in "Let us create man in our image"?
Elohim is a Hebrew word that is always plural in form and also always singular in meaning when used in reference to the God of Israel: God, not Gods. This is easy for us to confirm by consulting any English translation of the Hebrew Bible.
You’re right that angels are also called
elohim. One angel is
elohim (plural in form, singular in meaning). A group of angels, more than one angel, is also called
elohim (plural in form, plural in meaning). This is also easy for us to confirm by consulting any English translation of the Hebrew Bible.
We can also check this by consulting the equivalent words in Greek. When
elohim is used in reference to the God of Israel, or one angel, the equivalent Greek word is
theos - singular. When
elohim is used in reference to more than one angel the equivalent Greek word is
theoi - plural.
There has been much discussion over the centuries about who the “us” is. ”Us” is plural, “God” is singular. The “us” is generally considered by commentaries to be God’s angelic court.
God created man, alone, by himself. “Himself” is singular, not plural.
And how is a person fully God, yet fully man
The question was answered at the Council of Chalcedon in AD 451.
How is a woman impregnated by God?
Supernaturally, by the overshadowing of his spirit.
For that matter, how is God different from man?
God is unbegotten, man is begotten.
And in what ways are we the same?
I would point to Jesus as the ultimate example. Even so, difference remain.
I don't pretend to know the answers to any of these questions, but I think there are enough questions here to preclude us from pretending that we know what Jesus meant when he said "I and the Father are one"
Jesus supplies the answer in his prayer to God.
... or "before Abraham was born, I am".
It’s a preexistence question. There are two possibilities: literal preexistence or ideal preexistence.
And to answer your question, I don't have a definition for God, because I don't understand what God is.
God is a being who is the creator.