American English (specifically, GA) is my native language, so (without really reading all the other responses, which are probably better than mine):
1. "Homo" is more pejorative than "gay". Though you'd use "fucking" with it: "Fucking homo". But this would be someone calling someone else this.
2. I'd just use "faggot" here, though that has a connotation of self-deprecation in this scenario, if someone is describing themselves.
2.5. "Fifteen-year-old person" is fine. ("fifteen-year-old" is one phrasal adjective, so it gets hyphenated together to make it one "unit", whatever the real linguistics terms are). For that phrase, you spell it out; you'd use the numeral form with other things ("1970's-era music")
3. I'd say "last year of middle school"; there are schools in America where middle school goes through 9th grade (that is, the grade where people are 14–15 generally). I'd probably add "I start my first of three years of high school in the fall" to make the cultural note clearer, even if it's not a perfect translation
4. "It's slightly past three in the afternoon, and dinner ready soon". Again, you write out the number, though using the numeral isn't *wrong*, just weirder to me. Also note that "soon" tends to come after "ready", not before (to my ear). In casual speech, people tend to say "in the afternoon" instead of "PM", or just drop it altogether: if you tell someone you'll be having dinner at 3, they'll know you mean the afternoon (though that's an extraordinarily early time for dinner, to me; I think of the earliest you can have dinner as being about 4:30–5)
5. This sentence is perfectly fine to me. You can help yourself to something you cooked, and it doesn't have a negative connotation to me; it just means that you're serving yourself, and probably a larger helping. If you want to sneak the sauce name in, you can say "pork chops drowned in gräddsås, a light-colored cream sauce". Unless it's a culinary plot, I think you're fine with that level of detail. The actual name gives any curious readers the ability to google it.
6. Yes, you can open a window to air out a room. This sentence reads awkwardly to me. I'd probably say "The air in the room has gotten stale; I feel like it needs to be aired out."
7. Telly is British-ism. Here, we say "TV" or "television", probably the former.
7.5. I never remember the lay/lie distinction, so I can't comment on that.
7.75. Moist is a word in English that has a lot of negative connotations for some people. If "damp" is also reasonable, I'd recommend that, instead.
8. Nope, seems fine to me, though I'd rather some additional prepositional phrase or clause: "We've always stuck together through thick and thin" or "We've always stuck together despite our occasional fights" or something like that.
9. This phrasing is perfectly reasonable to me. "Little triangle" isn't particularly a slang word we'd use, so its meaning is a little obfuscated, but given context, it's clear. There's probably a more natural slang term that's just not coming to me right now.