If you are sitting down and someone is standing very close to you, you could say they are looming over you (especially if they are very tall). It has a negative connotation. That's not an unusual phrase or usage

The most common usage of the verb "loom" for native speakers is the fixed phrase "loom large", which is often used to describe a problem, threat, or important event that feels imminent or prominent (e.g., "Financial worries loomed large"). Other natural variations depend on context: "loom up" or "loom out" are used for something appearing suddenly or clearly (e.g., "A figure loomed up from the fog"), while "loom above/over" emphasizes something towering or threatening (e.g., "Mountains loomed above the village").

It's a rare word. I wouldn't say any usage of it is particularly common. The first 2 uses that come to mind, for me, are: the machine used in weaving textiles, and the Fruit Of The Loom clothing brand (based on the name of the weaving machine again). Having said that, you could say danger is looming, or the rain clouds are looming, etc. And you could say people are looming around. I don't think I've heard any of the phrases you suggested, but "looming above" seems like the more natural usage out of those options, to me.

Good question. The most common and natural use of loom today is in the expression “loom large.” Example: The deadline looms large in everyone’s mind. (meaning it feels big and important, often in a worrying way). Other forms like “loom up,” “loom out,” or “loom above” are also correct, but they are more literary or descriptive, often used in stories. Example: A dark mountain loomed above the village. So in everyday English, people mostly use “loom large.” The other variations are less common and usually appear in books or formal writing.

The verb is most commonly used as an adjective in its present participle form, eg. "the looming deadline". After that, the second most common use is paired with a modifier, usually an adverb, eg. "the dark clouds loomed large over the town". (Although "large" is normally an adjective, I would argue that it acts here as an adverb because it tells *how* the dark clouds loomed.) Less commonly, but not at all rarely, it can be used as a straightforward active verb, eg. "a storm loomed in the distance ahead of us as we drove west".