In America we never say that as a simple alternative to the more bookish "I have a car." We would use the contraction: "I've got a car." Although the difference is so subtle that it's really silly to be analyzing it in a discussion of colloquial speech.
You spend the evening with your friends in a bar. You're getting tired of the band playing nothing but 1960s soul music and 1970s disco (perhaps I'm recounting my last experience with a certain band but whatever...). About 1:30am Suzie says, "Hey I just remembered that a really good band is supposed to play at the after-hours club in D.C.. Let's go hear them!" George says, "That's too far to walk and the subway stopped running an hour ago." You say, "Oh crap, we need a car but we all walked here."
Suddenly Vicky walks out of the restroom and says, "I got a car!"
It's just a slangy way of expressing emphasis.
As for the other construction...
The gang in the office wants to go to lunch together. There are six of us. If we could take one car we can get back in the parking lot, but if we take two cars somebody will have snatched one of the spaces by the time we get back. Everybody seems to have a four-seat Japanese car and it looks like we can't go. I suddenly remember that since I have a dentist appointment after work, I drove my car today: A 4000-pound 1980 Mercedes diesel land yacht which will hold six people without too much discomfort. I turn to the gang and proclaim with great solemnity, "I have got a car."
It's something I say to build suspense. Everyone begins wondering just exactly what kind of car I have.
"I have been." The past participle tense "have been" is not further in the past than the past tense "was".
"I have been" is called the present perfect tense. Even I would probably not bother making this point on any other forum, but since it's linguistics.

The past perfect is "I had been." (Grammarians also call this the "pluperfect" but it's the same thing.) The future perfect is "I will have been." The conditional perfect is "I would have been."
The difference between the
preterit or simple past tense "I ate" and the
present perfect "I have eaten" is not a matter of which activity occurred further in the past. It is the relationship of the activity to the rest of the discourse. The preterit is simply a statement that an activity took place in the past and is completed. The present perfect says that the activity took place in the past but that fact has some impact on the present. "I'm not hungry enough to share that pie with you because I have eaten." "There aren't very many flowers left in my garden because your dog has eaten twelve of them."
In the sense of "must", "have got" can be future or future perfect: Future: You've got to be on time for the show tonight! Future perfect: English has got to be the hardest language in the world to understand!
This is not the future perfect. The future perfect of "be" is "You will have been on time."
"You've got to be on time" is just another colloquial way of saying "You have to be on time" which is just a colloquial way of saying "You must be on time." "Have to" and "have got to" are just used as unnecessarily intricate auxiliary verbs.
Sometimes these constructions don't make any sense if you take them word-for-word. Look at the standard French way of asking, "What is that?" --
Qu'est-ce que c'est que ça?" A literal translation goes: "What is that which that is which that?" There's a verb missing!