Yes.
Christians are those who believe that Jesus is God, the second person (hypostasis) of the Trinity and consubstantial with the God the Father and God the Holy Spirit.
Agreed. How do non-Trinitarians explain the following passage:
18 And Jesus came and said to them, “All authority in heaven and on earth has been given to me. 19 Go therefore and make disciples of all nations, baptizing them in[b] the name of the Father and of the Son and of the Holy Spirit, 20 teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.”
http://www.biblegateway.com/passage/?search=Matthew%2028&version=ESVUK