That is not true. I know of groups that are evangelical and maintain the Nicene creed. Furthmore, the SBC, which is the focus of this article, is cleary Trinitarian.
#2 Going on the above, do the groups you list hold to the beliefs in the Nicene creed (meaning saying "if you don't believe that Jesus died and rose from the dead (say), then you aren't in our definition evangelical"? I doubt that they do (though could be wrong).
#3 you are correct, the Southern Baptist are clearly those who believe in a Triune godhead, unlike the Pentecostals listed above