The phrase is colloquial. The correct way to say it as others have mentioned is "I've got," but if someone's a bit busy and speaking fast, it's not uncommon to hear something like this.

Grammatically speaking, it should be "I've got" instead of "I got". The former is the correct way to say "I have/own/obtain", whereas the latter means "what you had in the past" as you knew. I'd say this is either a careless typing or a casual way to say it. BTW, "I've got" is not that easy to be heard clearly and distinguished from "I got" in a spoken language sometimes.

I think you mean "have got". We use have got with noun phrases to talk about the future. Ex. I have got a hundred things to do tomorrow. I've got tons of homework. The 'got' isn't necessary. Both sentences would also be correct if the got was omitted.