1) The answer to your first question is; Yes!
John 16:7-15 (KJV)
7 Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you.
8 And when he is come, he will reprove the world of sin, and of righteousness, and of judgment:
9 Of sin, because they believe not on me;
10 Of righteousness, because I go to my Father, and ye see me no more;
11 Of judgment, because the prince of this world is judged.
12 I have yet many things to say unto you, but ye cannot bear them now.
13 Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come.
14 He shall glorify me: for he shall receive of mine, and shall shew it unto you.
15 All things that the Father hath are mine: therefore said I, that he shall take of mine, and shall shew it unto you.
2) To properly reference that question we need to correlate from within scripture! The text and context of your questions! When we read from another translation, as provided above; note that it says, “for he shall not speak of himself;” In the complete context from which this statement is made, Jesus is warning the disciples concerning the potential of deceptions by another spirit, not authorized to administer the gospel according to scripture through the Apostles and subsequent believers throughout the church age; after the Day of Pentecost, beginning in Acts 2. The following scripture references show; the instruction and a pattern of the problem from the Old Testament! As a personal example while with a street evangelism group our team came upon a particular individual that had an anointing of a familiar spirit and would quote scripture way out of context in order to justify the profane life style! If the group would attempt to share within a Biblical context; concerning his lifestyle he, would get violently angry and change the subject when confronted with scripture that the he had chosen to avoid!
Leviticus 20:27 (KJV)
27 A man also or woman that hath a familiar spirit, or that is a wizard, shall surely be put to death: they shall stone them with stones: their blood shall be upon them.
1 Samuel 28:7-8 (KJV)
7 Then said Saul unto his servants, Seek me a woman that hath a familiar spirit, that I may go to her, and enquire of her. And his servants said to him, Behold, there is a woman that hath a familiar spirit at Endor.
8 And Saul disguised himself, and put on other raiment, and he went, and two men with him, and they came to the woman by night: and he said, I pray thee, divine unto me by the familiar spirit, and bring me him up, whom I shall name unto thee.
1 Chronicles 10:12-14 (KJV)
12 They arose, all the valiant men, and took away the body of Saul, and the bodies of his sons, and brought them to Jabesh, and buried their bones under the oak in Jabesh, and fasted seven days.
13 So Saul died for his transgression which he committed against the LORD, even against the word of the LORD, which he kept not, and also for asking counsel of one that had a familiar spirit, to enquire of it;
14 And enquired not of the LORD: therefore he slew him, and turned the kingdom unto David the son of Jesse.
2 Chronicles 33:5-6 (KJV)
5 And he built altars for all the host of heaven in the two courts of the house of the LORD.
6 And he (Manassa) caused his children to pass through the fire in the valley of the son of Hinnom: also he observed times, and used enchantments, and used witchcraft, and dealt with a familiar spirit, and with wizards: he wrought much evil in the sight of the LORD, to provoke him to anger.
Isaiah 19:2-3 (KJV)
2 And I will set the Egyptians against the Egyptians: and they shall fight every one against his brother, and every one against his neighbour; city against city, and kingdom against kingdom.
3 And the spirit of Egypt shall fail in the midst thereof; and I will destroy the counsel thereof: and they shall seek to the idols, and to the charmers, and to them that have familiar spirits, and to the wizards.
Isaiah 29:3-4 (KJV)
3 And I will camp against thee round about, and will lay siege against thee with a mount, and I will raise forts against thee.
4 And thou shalt be brought down, and shalt speak out of the ground, and thy speech shall be low out of the dust, and thy voice shall be, as of one that hath a familiar spirit, out of the ground, and thy speech shall whisper out of the dust.
3) The Trinitarians belief is based on what is taught in scripture! In the following verse Daniel uses in his prayer, and throughout the remainder of his prayer; All Three of what is called The Trinity! (bold highlight mine)
Daniel 9:4 (KJV)
4 And I prayed unto the LORD my God (Y@hovah), and made my confession, and said, O Lord (‘Adonay), the great and dreadful God (‘el), keeping the covenant and mercy to them that love him, and to them that keep his commandments.
Genesis 24:2 (KJV)
2 And Abraham said unto his eldest servant of his house, that ruled over all that he had,
What we have here is a fore type of the evangelistic work of The Holy Spirit; as Abrahams servant was sent to get a wife for his son Isaac. In parallel fashion The Holy Spirit rules over the Kingdom of God on earth, in an administrative capacity during the church age. Drawing the lost to salvation; as Rebekah was invited to follow Abrahams servant back to her unseen husband to be. She was impressed by the testimony and gifts delivered by the servant; believing his word! The servant did not spend much time speaking of himself rather spoke of his master and his son with all authority, ability and privilege according to his commission.
In a more earthly comprehension; just look at an egg; three parts different capacity and function. An egg in a nest may be a bit unsanitary, when we reach in to pick up that egg we handle it with care, clean it, break it open and prepare for food (Bible study and prayer)! The Holy Spirit delivers the gifts and produces the fruit of the Spirit within us; as we submit to his leading, He is just doing the job He was sent to do until his work is finished!
John 14:23 (KJV)
23 Jesus answered and said unto him, If a man love me, he will keep my words: and my Father will love him, and we will come unto him, and make our abode with him.
What we have here is the ultimate goal of The Holy Spirit while on earth as we can comprehend it, The Holy Spirit desires for any believer to be visited by The Creator while still on earth!