AFAIK, from what I've read here what you saw and heard are common, allowable variations in Eastern Orthodox practice, including having members of the congregation, including women, chant the epistle.
Many of the Ukrainian Orthodox in the US were Ukrainian Catholics to begin with but they left the UGCC in the 1930s, not 15-20 years ago.
There are two reasons why there is a separate (from the Russian Orthodox) Ukrainian Orthodox church in the US.
First, in the Ukraine after the Russian Revolution there was a wave of nationalism and a separate church got started, but no Orthodox bishop would consecrate bishops for them. So they had a group of priests and the relic of a bishop's hand 'consecrate' their leader - so for decades they didn't really have apostolic succession! I think either this 'dead hand' group died out or somehow they got real bishops later. I think some of this group, under 'Bishop' John (Theodorovich), came to the States.
Second, the Ukrainian Catholics in the US were treated badly by the RC authorities and the last straw was after 1929 when, because the US RC bishops wanted it, the Vatican banned the ordination of married men as priests and said church property had to be owned by the bishop, which scared the people because they were used to dealing with hostile RC bishops who wanted to close them down. So these people formed Ukrainian Orthodox churches, I think sometimes when Ukrainian Catholic churches seceded and managed to keep their own property.
(This sad story mirrors how 60% of what's now the OCA got started around 1900 and how ACROD began in the 1930s - ACROD, like the UOC now, is under the Greeks of Constantinople. Like the majority in the OCA they're ethnic Ruthenians from the other side of the Carpathian Mountains from the Ukrainians.)
I think somehow these two Ukrainian strains met and formed a church. Technically it was vagante (not really in the Orthodox Church) for years... until about 15-20 years ago. The patriarchate of Constantinople took them and so today they are a real Orthodox church. Very nationalistic - I've been to them twice and what struck me was they used Ukrainian, not Slavonic which they share with Great Russians as their traditional liturgical language.
I've heard their liturgical usage varies a lot, along a spectrum from all Russian Orthodox practices to all Ukrainian Catholic ones.
I've met their archbishop for Chicago, Vsevolod, who's an ethnic Ukrainian from Poland (owing to changing borders). Very nice man, deep Slavic-accented bass voice, one of the most RC-friendly real Orthodox bishops there is ... and he looks a lot like Santa Claus with his white beard.
Birthgiver of God is just an odd-sounding, literal translation into English of the Greek Theotokos, usually rendered in English as Mother of God. It looks like a case of being needlessly different but those who insist on the different wording have a point linguistically in that, in Slavonic for example, there is another word literally for Mother of God, -ÃƒÆ’Ã‚Â¦-+-Ãƒâ€šÃ‚Â¦-+-+-Ãƒâ€šÃ‚Â¦-ÃƒÆ’Ã‚Â©-Ãƒâ€šÃ‚Â¦-ÃƒÆ’Ã¢â‚¬Â¡-ÃƒÆ’Ã‚Â®. Birthgiver of God or God-bearer is -ÃƒÆ’Ã‚Â¦-+-Ãƒâ€šÃ‚Â¦-+-ÃƒÆ’Ã¢â‚¬Â¡-+-Ãƒâ€šÃ‚Â¦-+-ÃƒÆ’Ã‚Â¥-Ãƒâ€šÃ‚Â¦.