Fantastic questions!
Unfortunately, as with all questions, the answer is ultimately “It depends.” Joseph Smith (Mormonism’s founder) was a fairly exploratory, adventurous person, but modern Mormonism is typically quite Protestant in its popular-level views. Many modern Mormon intellectuals typically gravitate toward what appears to be the view of God Smith articulated at the end of his life, that God is a distinct person, embodied like us in “flesh and bones,” gendered and sexed as male, implicitly with a wife (perhaps many; Brigham Young, Smith’s successor in the LDS Church in its more polygamous era, certainly thought so), who differs from a human being only in power and morality.
But there’s room for creativity here, too, as a lot of what Smith said and dictated was somewhat experimental, fluid, and whenever he was systematic (such as when he produced a body of text called the Lectures on Faith in the 1830s, a kind of early-Mormon catechism), it was almost immediately outdated by further ideas. I personally gravitate primarily to Smith’s creativity and imagination than any particular statements he made; so, while I appreciate his insights (for instance, his King Follett Discourse, his “sample of pure language” dictation, or his “Olive Leaf” text on a tripartite heaven), I believe they’re each superseded by his intellectual adventurousness: a “everything that follows is merely provisional” kind of approach.
Other Mormons take different approaches, though. Blaire Ostler, so far as I can tell, in constructing a queer Mormon theology, sees God in a very distinct plural, as multiple persons with occasional polyamorous overtones. Blake Ostler, an attorney and Mormon theologian, is somewhat similar in that, while he speaks of a literal God the Father and Jesus Christ, he typically means God in a communal, relational sense: God is a cosmic family of persons. Adam Miller, a professor of philosophy in Texas, has a quasi-Buddhist approach to Mormonism and tends to describe God in the same way a Buddhist would describe existence, that which they’re attempting to be one with; I doubt he would consider himself pantheistic, but I think he could certainly be read that way. And then there’s me: as I intimated in this piece, my view is somewhat Heideggerian (though I first got it from Eastern thought) in that I typically write about God in Mormonism as Heidegger’s notion of Being and each person as a being who is always already a part of that overall Being: the dilemma being that, for a number of reasons (many o them emotional and psychological), we don’t typically experience that willingness but experience ourselves as distinctly separate from others and the rest of the universe at large and thus either at war with them or at their mercy. As one Stoic put it, “Jupiter is all we see and experience”; I take a similar position on God, and thus we’re always already united with God by virtue of existing, let alone being alive (let alone being conscious even!); and how we think and feel about, and how we respond to “all we see and experience” is for me what I ultimately talk about when I talk about reunion or “atonement” with God in Mormon thought.
By contrast, general authorities in the LDS Church may occasionally reference God’s embodiment, but they typically refer to God exclusively as “Heavenly Father.” Relatively recently, the term “Heavenly Parents,” implying God the Mother (as mentioned implicitly by Smith and explicitly by Young, although in a polygamous context admittedly), has become more popular on an institutional level. Other than that, God is typically referred to in one of three modes: as a loving parent guiding the lives of his children, as a lawgiver expecting his children to push for whatever the modern LDS Church may interpret as ultimately moral (which can be a stick issue), and a religious restorer who has instituted distinct rituals (ordinances, in Mormon parlance) that one must receive in order to be “saved” or “exalted” or “return to live with God again” (this last bit can be somewhat fuzzy). This perspective, the institutional one, is usually used in missionary work and in the Church’s biannual General Conference; it also seems to be preferred by the average Latter-day Saint, who seems to be just looking for emotional stability in their life by going weekly to church services, attending a nearby temple on occasion, and “following the prophet.” However, I think this view can more often than not be exceptionally underwhelming and even harmful, even to those simply seeking emotional stability. Hence a good deal of my writing on Mormonism goes to trying to offer alternative perspectives and modes of speaking about “God” and other topics that I believe can be more helpful tools in developing emotional intelligence. That’s ultimately my own goal, as I intimated above: less to create any final, systematic way of looking at or talking about things, but finding whatever best helps us develop further emotional intelligence and to feel at home in our human condition here and now.
I definitely would be classified as neatly orthodox in my writing; in other words, were you to encounter Mormon missionaries, you’d likely find them somewhat trained in the more institutional perspective and not at all in the other perspectives I’ve mentioned, such as those of Ostler, Ostler, and Miller, as well as my own. Those hypothetical missionaries may simply not know how to address our views, they may classify us as just oddballs relative to the General Authorities of the institutional church, or they may even go so far as to see us as “apostate” and thus contrary to Christ’s “only true and living Church”; but when you take a bird’s-eye-view of Mormonism, it is most definitely a sprawling world of varying ideas, concepts, language, and practices. And that’s to say nothing of other denominations in the Mormon movement. Te LDS Church in which I grew up is the largest denomination, but then there’s Community of Christ, who are substantially different from the LDS Church in fascinating ways; and there are fundamentalist groups, many of whom still practice polygamy and hold onto Brigham Young’s belief that Adam/Michael is God the Father of our spirits before the creation and our bodies after the Fall, and who is the physical father of Jesus through Mary. It’s a big field, tough to summarize without focusing in on any particular group, but that’s kind of what I love about it, to be honest.
That’s an admittedly dense overview, but I hope it helps.
