The word "Apostolic" has and has had many, many meanings over the years.
There is a broad definition of "Apostolic" among members of this forum.
Baptism in Jesus' name to some means that the name "Jesus" with or without titles like "Lord" and/or "Christ" must be spoken during the ritual of baptism. Baptism in Jesus' name to others means baptism in the authority of Jesus or baptism as authorized by Jesus and would mean the words He spoke in
Mathew 28:19 to the ones who would do the baptizing would be spoken during the ritual.
Faith in Jesus Christ to some means a trust or commitment to Jesus which results in a desire to obey Him. Faith in Jesus Christ to others means a trust or commitment to Jesus which includes specific acts/works/rituals which those persons designate.
There are different beliefs among Apostolics on how/when a person is justified/saved/born again. Some believe a person is justified/saved/born again at repentance. Others believe a person is not justified until a person has repented, been baptized in water by immersion in the name of Jesus (with perhaps a title or two like "Lord" or "Christ). On this forum we refer to those two groups as one-steppers and three-steppers. The modern Apostolic/Pentecostal movement which began in the late 1800's and blazed into a world-wide movement was made up of one-steppers. They believed in the Holy Ghost Baptism by knew they were already saved before they received that experience. Later, when some began to practice and preach water baptism in Jesus' name, that experience was not considered to be part of getting saved. It was an experience for folks who were already saved. Later, water baptism and Spirit baptism began to be considered a "plan of salvation" and that belief has grown until today there are many Apostolics who believe it.
As far as belief in "one God," well the folks we label as "oneness" and the folks we label as "trinitarian" both believe in one God, they just explain it differently theologically.