Hi Teacher!

In formal writing, you'd address your teacher by their title (Mr./Mrs./Dr.) and surname.

I'm writing this because I'm want to say thank you for the last class, it was very interesting and useful.

Talking about another thingAlso, today I need to go to the pharmacy because I'm docompleting the process forto get my green card and because of that I need to have all my vaccinations, so, today I have to puget my second dosis of polio, ipolio shot. It's not fun, but it's neccessary.

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You may hHave a wonderful day!

I would refrain from using emoticons or emojis in any writing to my teacher because it's seen as too informal and casual.

You could reword the sentence to be "May you have a wonderful day" which is gramatically correct, but is rather unnatural. Sometimes a more straightfoward construction is best.

Hi Teacher!

I would usually address a teacher as "Mr. [surname]", "Ms. [surname]", "Dr. [surname]", or similar (depending on which title is appropriate); I would only address them as "Teacher" if I didn't know their name.

If this were a formal letter or email, you would also probably want to use "Dear" as a greeting (e.g. "Dear Teacher," "Dear Mr. [name]," etc.), and follow the name with a comma. But for your more conversational tone, "Hi" is probably the better choice.

I'm writing this because I'm want to say thank you for the last class, it was very interesting and usehelpful.

The word "useful" is associated with things that you "use" - for example, tools or devices - so it's a slightly unusual word for describing a class.

Strictly speaking, it would also be more grammatically correct to either split this sentence into two sentences, or to connect the clauses with a conjunction. To give a few examples:
"[...] the last class. It was very [...]"
"[...] the last class, which was very [...]"
"[...] the last class, as it was very [...]"
But the way you've written it is fine for a more casual tone, so I didn't mark it as a correction. (Other people might disagree about whether it's acceptable, however.)

Talking about another thingBy the way, today I need to go to the pharmacy because I'm doing the process for my green card and b. Because of that, I need to have all my vaccinations, so today I have to puget my second dosise of the polio, i vaccine. It's not fun, but it's neccessary.

"Talking about another thing" is acceptable English, but it sounds a little unusual. I'd probably use "by the way" here, but some other examples of common phrases include "on an unrelated note", "as an aside", or "changing the subject".

Your sentence is a bit of a run-on sentence. This isn't a major problem, as long as your teacher doesn't mind a casual tone, but it reads a little more smoothly if you separate it a bit.

In regards to "...my second [dose] of polio", your intended meaning is clear enough, and I probably wouldn't bat an eye if I heard it in conversation. However, in writing, I personally think it's better to be more explicit and say "the polio vaccine".

The phrasing of "It's not [x] but [y]" sounds odd to me, though I honestly don't have an explanation for why.

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Have a wonderful day!

"You may have a wonderful day!" sounds like a prediction - you're stating, "it's possible that you will have a wonderful day!"
Your intended meaning is probably closer to "May you have a wonderful day!", which essentially means "I hope you have a wonderful day!" (I think that, technically, the phrasing of "May you [...]" is an example of the "optative mood", but I'm only basing that on a quick Wikipedia search.)
However, the phrase "May you have a wonderful day!" would sound a little overformal, in my opinion. A simple imperative sentence is perfectly acceptable in this context.

I'm writing this because I'm want to say thank you for the last class, it was very interesting and useful.

Talking about another thing, todayOn another subject, I need to go to the pharmacy today because I'm doing the process forof getting my green card and because that I need to have all of my vaccinations, so today I have to puget my second dosise of the polio vaccine, it's not fun but it's neccessary.

On another subject sounds more natural

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Have a wonderful day!

You may have = allowing someone to do something (eg. you may have one piece of cake.), May you have = wishing someone something. May you have isn't necessary in this context though.