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The very early Jehovah's Witnesses (then called Bible Students) already believed that trinity and immortality of the soul were unscriptural.
As the book God’s Kingdom Rules! on page 24 says:
For centuries, the world of Christendom had been enveloped in spiritual darkness; many of its teachings were rooted in paganism. A prime example is the doctrine of the immortality of the soul. During the 1800’s, though, a few sincere students of the Bible scrutinized that teaching and saw that it had no support in God’s Word. Henry Grew, George Stetson, and George Storrs wrote and lectured boldly, exposing that satanic lie. Their work, in turn, had a profound impact on C. T. Russell and his close associates.
The little group of Bible Students found that other doctrines linked to the immortality of the soul were likewise confusing and false—for example, the teaching that all good people go to heaven or that God torments the immortal souls of the wicked in eternal hellfire. Russell and his close associates boldly exposed those lies in numerous articles, books, pamphlets, tracts, and published sermons.
Russell started his work in the late 19th century, so what was decades before.
Their stance on the trinity doctrine was already very clear in that period too as this article writes:
Through the pages of Zion’s Watch Tower and Herald of Christ’s Presence, Russell and his associates courageously denounced false religious doctrines that misrepresented God. They discerned that—contrary to popular religious opinion—the soul is mortal, that at death we go to the grave, and that Jehovah is the only true God and therefore not part of a Trinity.
Upvote:2
A problem with JW denial of the Trinity doctrine is that they present a warped version of what the Trinity supposedly teaches. In 'Thy Kingdom Come' published in 1891, p119, their first president, Russell, wrote that they "were guarded against the unscriptural as well as the unreasonable theory that Jehovah is his own Son and our Lord Jesus is his own Father". Well, that is not what the Trinity doctrine teaches! That is Russell's misunderstanding of the doctrine!
On the second topic you ask about, Russell immediately followed the quote above with: "and they began to see that eternal life and immortality are not present possessions, but are to be expected only as the gifts of God through Christ in the resurrection." However, bear in mind that Russell did not have the belief of soul annihilation that came later, and he taught that millions would also be in heaven in addition to the special 144,000 class.
Before the NWT came out, JWs did not have had a recognisably orthodox Trinitarian belief, yet for over 50 years they had advocated worshipping Jesus Christ as God, which is absolutely Trinitarian! It wasn't until 1954 that JWs were told they should no longer worship Jesus. Yet the Society’s Charter was not changed until 1999, removing the bit about the purpose of the Society being the worship of Jehovah AND Jesus Christ. They left it just as for the worship of Jehovah.
They were worshipping Jesus in the 1930s as these quotes show: "During the Millennium, "the princes will lead the people in their worship of Jehovah and of Christ." (Vindication Volume 3, p295, J. F. Rutherford, 1932) “Jehovah God commands all to worship Christ Jesus because Christ Jesus is the express image of his Father, Jehovah, and because he is the Executive Officer of Jehovah always carrying out Jehovah’s purpose (Heb.3-6).” Watchtower 1939 Nov. 15 p.339 click for scan http://www.jwfacts.com/images/watchtower-1939-nov-15-p339 [Read Only]
They were still worshipping Jesus in 1945 as this 15 October 1945 Watchtower shows: “Now, at Christ’s coming to reign as king in Jehovah’s capital organization Zion, to bring in a righteous new world, Jehovah makes him infinitely higher than the godly angels or messengers and accordingly commands them to worship him... Since Jehovah God now reigns as King by means of his capital organization Zion, then whosoever would worship Him must also worship and bow down to Jehovah’s Chief One in that capital organization, namely, Jesus Christ, his Co-regent on the throne of The Theocracy.”
Their 1945 Yearbook includes the Charter in full. Part of the then current charter stated as follows: “…maintain and send out to various parts of the world Christian missionaries, teachers and instructors in the Bible and Bible literature and for public Christian worship of Almighty God and Christ Jesus; to arrange for and hold local and world-wide assemblies for such worship...” Click here to scan http://jwfacts.com/images/watchtower-yearbook-1945-page-32.jpg
But the first clear statement that Jesus must not be worshipped was in 1954, as far as I can tell. The 1 January Watchtower, page 31 said: “Should we worship Jesus? ...Consequently, since the Scriptures teach that Jesus Christ is not a trinitarian co-person [sic] with God the Father, but is a distinct person [which the Trinity agrees with!] the Son of God, the answer to the above question must be that no distinct worship is to be rendered to Jesus Christ now glorified in heaven. Our worship is to go to Jehovah God.” Yet it wasn’t till 1999 that the Charter was changed, to confine worship to Jehovah alone, according to this link! http://www.jwfacts.mobi/watchtower/worship-jesus.php
I have majored in answering your query about their rejection of the Trinity doctrine, to show that despite later claims that they dropped it in the far past of their history, there is a clear contradiction in the way they did not drop the worship of Jesus as God until 1954. They were far quicker to move on to soul annihilation. Both those doctrines were accepted before their NWT was published at the end of the 1950s.