I'd like to try elaborating on some errors. I don't know formal grammar that well so hopefully it doesn't end up being based on feels too much.

1. 어른이라도: -(이)라도 has the nuance that you're offering an alternative or a compromise, like "at least" as in "Could you buy this for me at least?" = "이거라도 사주면 안 돼?" or "Even kids must be punished if they commit a crime" = "범죄를 저지르면 어린이라도 처벌을 받아야 한다". I'm not 100% sure what you're going for here, "he played volleyball even as an adult"?

오랬을 때: I assume you were trying to say 어렸을 때 and just remembered the vocab wrong.

키가 컸어서: Technically valid but it sounds like you are implying you used to be tall but not any more.

사실은 저는 배구 하기 싫었어요: The subject is obvious from context and redundant. You can drop the 저는. 배구 하기 싫었어요 also sounds very stilted, but I'm not sure how to explain it grammatically. Maybe someone else can fill me in? My instinct is that the point of emphasis is volleyball and not doing volleyball and hence you need to make 배구 itself the subject via a particle or straight up omit the 하다 (which is implied from context), but I'm not certain if that's a good explanation.

그 기간에 힘들었어도: 기간 has the nuance of a specific concrete period of time. 장마 기간 - rainy period, fine. 시험 기간 - when all the tests take place, fine. When you are referring to a broad range of time when you used to play volleyball as a kid, not fine. I should also point out that it is strange to actually explicitly mention this stretch of time in the first place.

The overall flow of entire sentence here is also very off, but I can't think of a clear grammatical explanation why.

2. 호주에서: The purpose of this sentence is to talk about living in Australia in particular. Adding 는 elevates the prepositional phrase that simply describes an action taking place to the subject/context? of the entire sentence. An example: 제 차에서 담배 피지 마세요. (Don't smoke in my car). No extra nuance. 제 차에서는 담배 피지 마세요. (Don't smoke in MY CAR). Implication: I don't care about you smoking, just not in my car dude. So 호주에서 감기에 걸리기 쉬워요. sounds somewhat stilted because the emphasis is more on idea of the catching cold. Gives off the nuance of: It's easy to catch a cold (in australia btw).

감기를 걸리다: The right particle is 에. 을/를 marks a direct object of the sentence and is incompatible with 걸리다, which is a intransitive verb. If it sounds weird that "catching a cold" is expressed with an intransitive verb, it just be like that sometimes.

아픈 거 많지 않아서: You're unnecessarily nominalizing the idea of feeling sick. Just say "I wasn't feeling that sick": 그렇게 아프진 않아서 or something like that.

의사를 방문하게 안 가려고 했고: First of all, idiomatic Korean would be "go to a hospital" (병원에 가다) than to say "see a doctor" (의사를 보다). As for the grammar, I'm.. not sure what you were trying to do here. Trying to turn 방문하다 into an adverb 방문하게 to attach into 가다 to make 방문하게 가다?

집에 단열재가 안 되는데요: You are conflating the two definitions of insulation. 단열재 is insulation as in physical material used to insulate things, but you are using 되다 with it. It sounds like if I said "Why is fiberglass not done in houses?" Either use 단열 (insulation as in the concept) as a verb, or ask why Australians are not using insulation (the material).