Осень нНаконец-то придётнаступила осень.

Actually, this phrase is okay, but it's a bit uncharacteristically for Russians to say so. You can also write "Наконец-то пришла осень" or "Осень наконец-то пришла".

Как я сказала ранее, это лето - самое худшее, потому что я никуда не могла поехать и я была дома весь день.

"Как я сказала ранее" is quite official, you'd better write "Как я уже сказала" or "Как я уже говорила" - "like I've already said".
About the part with being at home all day long: in Russian you don't have to have a subject in every phrase. "никуда не могла поехать" and "была дома весь день" both depend on "я", they are similar.

Я хотелачу пойти в школу как можно скорее и, а школа начинается на следующей неделе.

In your whole text you have a hesitation with tenses: in the first one it's future, in the second - present, and the third consists of both future and present. It's incorrect as "я хотела пойти в школу" is about past - I wanted to go, and now either it has happened or I stopped wanting. "Школа начинается" is future, it only will happen, you're looking forward to it, but according to the previous phrase your will is already over.
If you're talking about present time, you'd better say "Я хочу пойти в школу... а она начинается только на следующей неделе" so you're looking forward to going to school and waiting for it.
We use comma between this two phrases because it's a so-called complex sentence: "Я (подлежащее) хочу пойти (сказуемое)" and "школа (подлежащее) начинается (сказуемое)" can both be standalone. However, we used "a" instead of "и" because I honestly see a bit of contradiction in here - I want to go to school right now, but I have to wait for a week!

Я нервничаю не только потому, что я буду изучать новые вещи, но и потому, чтоиз-за коронавируса.

In Russian there is a complex conjunction "не только,.. но и..." and I love the way you used, it's right!! (Secretly saying, not every Russian student can use it correctly))).
"Я нервничаю потому, что я буду изучать" - here you can just let go of the second "Я" as "Я нервничаю" and "я буду изучать" actually have the same subject - you, and you talk in your point of view so everybody gets the point without the second "я". It's sometimes difficult for foreign students not to use a lot of repetitions - Russians try not to say a lot of same words next to each other using synonyms instead.
About "из-за". It means "because of" and just like in English we'd better use a noun after.

Мы не знаем ес, будут (ли) учителя будут преподавать онлайн или лицом к лицу.

Мы не знаем (чего? What don't we know?), будут (ли) учителя преподавать онлайн или лицом к лицу. The second part is an answer on the question raised in the first part, so the first phrase is major and the second one is minor depending on the first.

Осень наконец-то придёходит¶
или¶
Осень наконец-то наступает

I'll try to explain in English, hopefully it will be fine;
Your phrase is good and correct, but it creates a feeling that you are speaking about quite distant future. For instance,
"когда осень наконец-то придёт, будет не так жарко"
From the context of your text, I assume that you are writing about the present, not about the future. But if you meant the future - then your phrase is absolutely correct and fully in place.

Как я сказала ранее, это лето - самое худшее, потому что я никуда не могла поехать и я была дома весь день.

Again, your phrase is fully correct;
However, usually you can skip identical pronouns, when you use them repetitively, like here. Note: it is better to keep "я" both in phrases "Как я сказала ранее" and "я никуда не могла поехать", but omit in "я была дома весь день". "Как я сказала ранее" is kind of a separate part of the sentence, and does not fall into that "repetition" pattern. For example, when you say something like: "Every day I wake up, then I go to school, then I go for a walk, then I come home and do my homework" (my example is silly, I know), in Russian you usually use "Я" only in the first instance: "Каждый день я просыпаюсь, потом иду в школу, потом иду на прогулку, потом прихожу домой и делаю домашнее задание".

Another thing: "весь день" means "the entire day", from morning till evening. If it what you wanted to write, than this is perfectly correct. But if you wanted to emphasize that you were indoors the entire day every day during the summer, the better way to express it is: "я была дома целыми днями".

Я хотела пойти в школу как можно скорее, и школа начинается на следующей неделе.

As I myself not excellent in punctuation, I don't try to comment on it... mostly. But here the situation is simple enough: in two parts of your sentence, there are two different subjects: "Я" and "школа". In this situation, you separate these parts with "," even if you use "и" between them...

Я нервничаю не только потому, что я буду изучать новые вещи, но и потому, чтоиз-за коронавирус.а. ¶
¶

Again, your text is correct, but there is a little thing:
Usually in this kind of phrases, if you use "потому, что ...", a verb is expected after. For example, "потому, что коронавирус распространяется", "because the coronavirus is spreading". If you want to put a single noun, it is somewhat better to use "из-за" and the noun in genitive case (в родительном падеже). Your option is not incorrect, but it adds a flavor of spoken language, where people tend to shorten phrases, and even make them a little bit strange for amusement and meme references :)

A little addition: phrases "потому, что..." and "из-за того, что..." are nearly identical in usage. So, you can write:
"из-за того, что коронавирус распространяется"
but
"из-за коронавируса"

Мы не знаем ес, будут ли учителя будут преподавать онлайн или лицом к лицу.

Here is the case when the words order is somewhat rigid. Phrases like "if teachers will teach..." are translated like "будут ли учителя преподавать..." nearly always.