There seems to be something of an answer in this article by Ian Sellers, published in 1977 in the book I quote from, below. I do not know if Ian Sellers is (or was) a Unitarian, however. He does not say, in his article. What is particularly helpful in his article is tracing the development of the modern 16th century movement. This, in itself, explains the difficulty of trying to pin any one, clear doctrine of God to Unitarianism. Here is what the article says:
"Unitarianism rejects the idea of the Trinity. It questions belief in
the divinity of Christ and of the Holy Spirit in favour of the oneness
of God. This idea was found in the early church, particularly in the
Monarchianist heresy. The modern movement dates from the early
sixteenth century. Renaissance ideas combined with some extreme
teaching in the Radical Reformation to produce Unitarian ideas in the
minds of many individuals...
Two prominent centres of early Unitarianism were Poland and Hungary...
Unitarian congregations sprang up [from 1558] and were known as the
'Polish Brethren'. They were formally organized in 1565, and became
known as the Minor Church. After 1574, when Faustus Socinus became
their leader, Unitarianism spread quickly. Its intellectual centre was
Racow. There a Polish Unitarian declaration of faith, the Racovian
Catechism, was published in 1605...
By the later eighteenth century Unitarianism in Hungary had been
almost completely suppressed... But in the rationalistic atmosphere of
the eighteenth century, very many English Presbyterian and General
Baptist churches began to be affected. They adopted first Arian, and
then Sabellian, Socinian or full-blown Unitarian ideas. Both became
largely Unitarian denominations by the second half of the eighteenth
century. The first self-styled Unitarian church, Essex Chapel in
London, was opened by the liberal Anglican Theophilus Lindsey who left
the Church of England in 1773. [Unitarianism] was legalized in 1813...
Meanwhile there were theological changes in Unitarianism." The
History of Christianity, page 495, Lion
On the next page details are given of Dr. Joseph Priestly, the English Unitarian minister, who rejected the doctrine of atonement and the Trinity and who had to flee to the United States in 1794 due to his support for the French Revolution. He and his successor, Thomas Belsham
"...found their source of authority in Scripture. They interpreted the
Bible in a rationalistic and optimistic way, to get round those verses
which Christians had previously used to support the doctrine of the
Trinity and the belief that man has a fallen nature. But in the 1830s
James Martineau and some younger Unitarians led a revolt against
biblical Unitarianism and its dogmas. They advocated a less
argumentative religion. They wanted a more refined, romantic and
devotional spirituality. They found religious authority in reason and
conscience, rather than in a biassed interpretation of Scripture.
Henceforth the Unitarians were rather sharply divided into an
older, 'biblical', and newer, 'spiritual' wing. The new group was well
on the way to eclipsing the biblical wing by 1850.
In Ireland... in 1830 the 'Remonstrant Synod of Ireland' was formed..
and are today more conservative in their beliefs than English
Unitarians. In North America... King's Chapel, Boston, became in 1785
the first Unitarian church in the New World.... In 1816 the famous
divinity school of Harvard was founded. It became the centre of
Unitarian thought. In 1825 the scattered Unitarian congregations
organized themselves into a denomination." (Ibid. p 450)
This skeleton (with a few bones missing) is vital to first have before trying to flesh it out with any modern Unitarian statements of belief about the God they worship. They have had a long history of persecution and, even today, they seem uneasy at answering any questions such as, "Are you anti-Trinitarian?" or "Do you worship God as a Person?" That is because nobody is bothered if there are varieties of belief, just so long as there is agreement that the Trinity doctrine is wrong, and that the Bible can be taken however one sees fit. That is not merely my opinion. Here is another quote, from Rev. Arthur J. Long, Principal, Unitarian College, Manchester, writing in the book below:
"Unitarians have always been suspicious of abstruse dogma,
repudiating the Trinity, and placing supreme emphasis on the unity and benevolence of God. Jesus Christ is not thought of as a
personal manifestation of the Deity, and although at first some could
accept him as a heavenly messenger worthy of adoration, later
Unitarians came to regard him primarily as a supremely gifted but
unequivocally human religious teacher and prophet. Correspondingly,
the basic assumptions of Christian 'salvation' are now generally
Unitarians believe in the general goodness of human nature and see
something of God in all people. The death of Jesus is thought of as an
inspiring example of dedication and self-sacrifice. The earlier
Unitarians accepted the notion of a physical resurrection, but most of
the story is now interpreted in a symbolic fashion.
Although most Unitarians nevertheless still regard themselves as
Christians, some - particularly in the USA - have now espoused a
non-theistic form of religious humanism, and among all Unitarians
there is an increasing tendency to look to other world faiths and not
merely to the Judaeo-Christian tradition. The imposition of fixed
creeds in religion is in any case regarded as unacceptable, and in the
English-speaking Churches especially, no confession of faith is
required of either ministers or members. This has resulted in a ready
acceptance of a wide variety of differing beliefs, practices, church
architecture and forms of worship." The Encyclopedia of World
Faiths, p136, Eds. Bishop & Darton, MacDonald Orbis, 1987 (All emphases mine)
Conclusion: The questions asked are actually answered in that last quoted paragraph, stated by an accredited Unitarian teacher and lecturer. But the background history also shows in the development of Unitarianism why there came to be a big split from what is called Biblical Unitarianism, so that the greatest variations in answers will be found by comparing that small group with the 'spiritual' or humanist group.