What’s the difference between I got (something) and i’ve got (something)?
Examples. I got a headache or I’ve got a headache. I got a big family or I’ve got a big family.

I know that GOT is the past form of verb GET. For example I got a student’s book. Meaning: School librarian or someone gave this me in past.
I got the job yesterday. Hooray!

But why do some people often say GOT, when they should use HAVE GOT?

Next.

Why does Ellen say And I GOT you nothing in this video ?

https://drive.google.com/file/d/19kkgreJU_fcDCSZdukM9Jk0syoA5auxt/view?usp=drivesdk
Why does she doesn’t say I’ve got? And why does she doesn’t say FOR? I’ve GOT something FOR you.This is grammatically correct.But she doesn’t speak correctly, does she? Why?

In this song Taylor Swift sings it’s like I GOT this music in my mind, saying it’s gonna be alright.
https://drive.google.com/file/d/1GcSqVAbvN-K2I27xLRKlLd3gaH5qnAgd/view?usp=drivesdk
Why does she says I got, not I’ve got?

In this video Hugrid says GOT something for you. Why? Is this correct? https://drive.google.com/file/d/1eymimhUqE4QGamLwHooAG042U4ywuoAF/view?usp=drivesdk

Question

What’s the difference between I got (something) and i’ve got (something)? 
Examples. I got a headache or I’ve got a headache. I got a big family or I’ve got a big family.

I know that GOT is the past form of verb GET. For example I got a student’s book. Meaning: School librarian or someone gave this me in past. 
I got the job yesterday. Hooray!

But why do some people often say GOT, when they should use HAVE GOT?

Next.

Why does Ellen say And I GOT you nothing in this video ?

https://drive.google.com/file/d/19kkgreJU_fcDCSZdukM9Jk0syoA5auxt/view?usp=drivesdk
Why does she doesn’t say I’ve got? And why does she doesn’t say FOR? I’ve GOT something FOR you.This is grammatically correct.But she doesn’t speak correctly, does she? Why?

In this song Taylor Swift sings  it’s like I GOT this music in my mind, saying it’s gonna be alright. 
https://drive.google.com/file/d/1GcSqVAbvN-K2I27xLRKlLd3gaH5qnAgd/view?usp=drivesdk
Why does she says I got, not I’ve got?

In this video Hugrid says GOT something for you. Why? Is this correct? https://drive.google.com/file/d/1eymimhUqE4QGamLwHooAG042U4ywuoAF/view?usp=drivesdk

Answer

It’s simply a reduction, where the auxiliary verb “have” (or “has”) is reduced to “‘ve” (or “’s”) and is eventually reduced all the way to nothing (in pronunciation). Americans talk like that all the time, although it would be a mistake to omit the auxiliary verb in writing.

I haven’t heard the song, but “I got you nothing” is perfectly correct as far as the grammar. It is the past tense of “get”. We can use a noun without a preposition as an indirect object — it must be after the verb and before the direct object. Other examples: You wrote me a letter / You cooked me dinner. This usage predates the use of prepositions; it used to depend on case endings, and today depends on word order.

Answer

As the others say, If you are being grammatically correct . . . .

I got = I received, procured, bought, etc. (the past tense of GET).

I've got = I posses, have, own, etc.

However, people very frequently used I GOT to mean the second one as well, even though it is technically not correct.

Answer

Хороший вопрос!

Often, "I got" is just slang usage.
It is not proper grammar, but it is the way that normal people speak.

But sometimes, "I got" is correct grammar.
For example,
"I got hot in the sauna."
or
"I got a gift for my birthday."

There are reasons for this, but I am not a professor, xaxaxa.

لا تفوّت فرصة تعلّم لغة جديدة وأنت مرتاح في منزلك. تصفّح مجموعتنا المختارة من مدرّسي اللغات ذوي الخبرة وسجّل في درسك الأول الآن!