This question covers a great deal of ground, so I will only be able to give a short answer to each of the points.
SELF-EXISTENT:
To be self-existent means to be the source of your own existence; to be the source of your own life.
Exodus 3:14 And God said unto Moses, I AM THAT I AM: and he said, Thus shalt thou say unto the children of Israel, I AM hath sent me unto you.
Here, God identifies Himself as the I AM. That title refers to His self-existence. He is of Himself without any other. Here are some other verses:
- Deuteronomy 32:40 For I lift up my hand to heaven, and say, I live for ever.
- John 5:26 For as the Father hath life in himself; so hath he given to the Son to have life in himself;
Notice that the Father has life in Himself. His life does not come from an external source. It comes from within Himself. He is self-existent.
ETERNAL:
- Psalm 90:2 Before the mountains were brought forth, or ever thou hadst formed the earth and the world, even from everlasting to everlasting, thou art God.
- Isaiah 57:15 For thus saith the high and lofty One that inhabiteth eternity, whose name is Holy; I dwell in the high and holy place, with him also that is of a contrite and humble spirit, to revive the spirit of the humble, and to revive the heart of the contrite ones.
I believe these verses are self-explanatory.
SPIRIT:
- John 4:24 God is a Spirit: and they that worship him must worship him in spirit and in truth.
- 1 Timothy 1:17 Now unto the King eternal, immortal, invisible, the only wise God, be honour and glory for ever and ever. Amen.
That He is "invisible" shows him to be Spirit.
TRINITARIAN:
This one involves much study, so I will only touch on it. Here are some verses:
- Matthew 28:19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
- John 10:30 I and my Father are one.
- 2 Corinthians 13:14 The grace of the Lord Jesus Christ, and the love of God, and the communion of the Holy Ghost, be with you all. Amen.
- 1 John 5:7 For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one.
The doctrine of the trinity is built on two facts:
- There is one God.
- The Father, Son, and Holy Ghost are all called God and have all the attributes of God.
Therefore, God is a three-in-one entity: one God in three persons. The Father initiates. The Son executes. The Spirit enables.
