Did JWs believe in trinity and immortality of the soul before they got their own Bible? This is a question about the Bible translation called the New World Translation of the Holy Scriptures (NWT) that was produced by Jehovah's Witnesses as a complete Bible first in 1961, and about its effects on doctrinal parts that in my opinion are more "foundational" (i.e. they have an effect on other doctrines).

In particular I wanted to ask about the concept of trinity and the immortality of the soul.

Did Jehovah's Witnesses believe in trinity and immortality of the soul before they got the New World Translation?
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.