Two principles spring to mind: clarity and discoverability.
First off, in writing a post you're trying to communicate to an audience. Or to audiences. As a question writer your audience is "the universe of people who might see this and give me a helpful answer." As an answer writer your audience is "the querent." But it's also often "the long tail of visitors and readers who will ever see this post." (See We're working on a new stat... esp. at "You've got to get this to get us.")
What abbreviations to use, then? Well, it depends on your audience. If you're writing a question and want to use commonly-used abbreviations in your game, go for it. Remember that you may end up limiting those who feel drawn to answer the question the more you use jargon: that may be a desired outcome, depending on your use-case, or it might be a detriment. Your call.
If you're writing an answer I'd say it's completely reasonable to use any abbreviations used in the question. Not only is the querent familiar with them, but it's fair to assume that future readers of your answer have also read the question. (And if not I'm less worried about their opinion.)
Part of making this the greatest repository of RPG-related Q&A the world's ever seen is making sure it gets seen! To that end discoverability is important for posts, too. I have a hard time imagining, for instance, the abbreviation LTH (used exclusively) helping a post get seen by someone searching the site or the internet for Leomund's tiny hut. If the hut's going to be mentioned thirty times feel free to abbreviate it twenty-nine of those times. But write it out the first time.
D&D/DnD/&c., on the other hand, are explicitly part of how our site organizes itself: look at our tags, after all! Abbreviations like AC, HP, DnD,... being ubiquitous through posts and site mechanics makes these pretty safe for discoverability. Your SP may not be another's SP, though, so that one's worth spelling out once or twice. THHGTTGTTRPG? Your guess is as good as mine =)