I've noticed that I tend to use the same three-step paragraph structure whenever a character is in a conversation then does action or vice-versa. It's something like this: Sensha and Howl picked up their pace, jogging up the hill after them while Sensha noticed that Mako had stopped dead in the snow. Her breath skipped when she got close enough to pick out the stocky person sitting on Naga's saddle, holding the reins tightly with a hood almost completely obscuring his face. Even from this distance she could spot his green eyes though. She found herself breaking into a outright sprint, not caring that her legs quickly started to burn with the effort of powering through the thick snow while going up a steep rise. See what I mean? First starts with the character's name, the second starts with a objective pronoun and the last with the personal pronoun. Is that good paragraph structure or is it frowned upon?
I wouldn't have noticed it if you hadn't told me. As far as I'm aware, paragraphs are separated based on subject: You start a new paragraph when switching between different characters (or groups) and when you switch between describing character (and environmental) actions. Additionally, I separate individual actions (or sets/chains) into separate paragraphs, though I'm not sure if this is proper practice. Using that logic, you would say that Sensha picked up the pace with Howl in tow, saving yourself the trouble of mentioning her a second time in the same line. The separation you've used seems fine, but I'd personally reword the last line for economics more than anything else. ...Ignored the burn of fatigue as she powered up the snow-covered rise kind of thing.
A paragraph usually introduces a new idea or a new speaker. In fiction, there aren't any set rules about when to introduce a new paragraph. A paragraph may have multiple ideas and/or speakers. If you aren't sure when to bend the "rules", just stick to conventional guidelines. In your example, I would only use one paragraph, but that's just my personal preference.
The pattern I'm seing is a sentence pattern of "Character verbed, verbing." (picked up their pace, jogging; got close enough, holding; breaking into a sprint, not caring) There's nothing inherently wrong with this pattern, or with the paragraph pattern that you describe, but there is something wrong with repeating the same structure too often. You want to introduce some variety.
Other than for dialogue, for me a paragraph change is to denote a significant change of focus or information from what was previous. Exactly what I mean by 'significant change' isn't easily defined, and for other authors it will come down to what they interpret it to mean. In the OP example, I would have all three paragraphs as one as I don't feel any significant change in focus has occurred.
never, never, NEVER follow such formulae in writing fiction... it's not called 'creative' writing for nothing... what you're doing would result in the most boring read imaginable, imo... in answer to your specific questions: no yes
Tbh mate, I think you could just class this as part of you're style, such as how some writers begin introducing the whole setting and then dialogue where as others do the opposite.