And yet they do not have a piano or instrumental music in their churches because they believe it to be unbiblical.
Apologies if I am confusing them with another group
You are. There is a difference between Church of Christ and United Church of Christ. Very different doctrines and the “Unitted has a central organizing body where the Church of Christ does not. The latter are basically independent congregations.
No, you are correct. They must just gloss over the whole book of Psalms.
On paper I’m still a UCC “Church” member. They use pianos, instrumentals, etc. It is a very loose origination so some local churches could have that restriction.