Defining God the Father attributes and defining Jesus' attributes

I'm always studying and there is no better way to worship the Father and the Son than through studying The Word. In Malachi_3:6 For I am the LORD, I change not; therefore ye sons of Jacob are not consumed.

and also this: Hebrews 13:8 Jesus Christ the same yesterday, and to day, and for ever. So let's use God's Word and NAME their attributes.

And Jesus quoted from the Old Testament:
Deu 6:4 Hear, O Israel: The LORD our God is one LORD:
Deu 6:5 And thou shalt love the LORD thy God with all thine heart, and with all thy soul, and with all thy might.

Lev 19:18 Thou shalt not avenge, nor bear any grudge against the children of thy people, but thou shalt love thy neighbour as thyself: I am the LORD.

Mar 12:29 And Jesus answered him, The first of all the commandments is, Hear, O Israel; The Lord our God is one Lord:
Mar 12:30 And thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind, and with all thy strength: this is the first commandment.
Mar 12:31 And the second is like, namely this, Thou shalt love thy neighbour as thyself. There is none other commandment greater than these.

So Here I want to start with an attribute of God the Father and of Jesus Christ:

Creator: There was never a time when God did not exist. Before there was anything at all, even time, God existed. No one made God. God made everything, from the tiniest subatomic particle to the farthest galaxy in the universe. Everything came from God, what we can see and what we cannot see — heaven, angels and the whole spiritual realm. He spoke and all these things came into existence. God alone is able to bring something out of nothing.

Joh 1:1 In the beginning was the Word, and the Word was with God, and the Word was God.
Joh 1:2 The same was in the beginning with God.
Joh 1:3 All things were made by him; and without him was not any thing made that was made.

God the Father and God the Son were together from the beginning. True or False? But where they two or one? What are their differences and what are their similarities?

Hoping this post will be a discussion and verse quoting on God the Father's and Jesus' attributes and perhaps, even how this knowledge affects our faith and walk.

Since you quoted from John 1:1-3, the answer was right there.

GOD = GOD THE FATHER
THE WORD = GOD THE SON
And in Genesis 1:1.2 we have the Holy Spirit also involved with creation.

So here we have two distinct divine Persons. But even though the Godhead (Father, Son, and Holy Spirit) was involved with creation, creation was in fact delegated to the Son, who is the Word, who is the Lord Jesus Christ, who is God, who is the Creator, who is also the Savior.

What we learn from all these Scriptures is that ELOHIM or THEOS (God) is in three Persons, Father, Son, and Holy Ghost, yet ONE GOD. Can humans comprehend this? NO. Can Christians believe it? YES. Those who refuse to believe that Jesus is God and that God is the triune Godhead cannot be saved. Why? Because only God Himself (as sinless Man) could take away the sins of the world.

Is there any attribute that they, God the Father and God the Son do not share?

Oh good question, actually quite profound.

None that they do NOT share. God is ONE yet three Persons.

For there are three that bear record in Heaven, the Father, the Word, and the Holy Ghost: and these three are ONE. (1 John 5:7).