Gonna = going to
Wanna = want to
Gotta = (I've)got to
Hafta= have to
Coulda= could have
Shoulda= should have
Wonlda= would have
Musta = must have
Lotsa= a lot of
Sorta = sort of
Kinda= kind of
That's not entirely true, EvanZhang.
When English speakers are talking in a rapid and relaxed way, we naturally drop consonants and run words run together, with the result that what we say sounds like 'gonna' and 'wanna'. When written down, these 'words' are just a shorthand form to suggest the sounds that we make.
Writers of cartoon dialogues and film subtitles sometimes use these shorthand forms to show that the characters is speaking quickly or in a casual way. Writers of popular songs also use them so that the words fit neatly into the music.
English speakers in their daily lives DO NOT usually write these as words, even in informal contexts. It looks lazy and childish to write them. Take a look through the pages of this site. You will see that all the people who use 'gonna' and 'wanna' in their posts are non-native learners of English. They, like you, mistakenly believe that their English will sound more native if they use these forms. But if you look at the posts written by American, British, Irish, Canadian, South African, Australian and NZ members, you will see that we always use the full form - want to, going to and so on. Now do you believe us?
Don't use them. They all sound childish when written. Don't write "u" instead of "you" either. It's rather annoying.
"...natives speakers always use words like gotta/wanna and stuff."
Well, no not really. We all understand what standard, regular English is and we use that as our default when communicating with other native speakers. I don't know if you've realised, but my two examples are distinctly Australian (one is an Australian catchphrase from a commercial) and native speakers would probably pick up on this difference. However, I simply wouldn't use them with native English speakers from other countries because, unless I know those people already, I assume they just won't get my meaning.
Basically, you would never use these slurred forms if you don't know the other person - it would just make you appear ignorant. You really have to give a thought to who will listen to you or read your message.
For example, "I wanna know... " (which is a phrase I often see written by learners but not by native speakers) is not appropriate because the writer is asking a community - and many of these members would also be strangers to a degree - for help in a public forum. So, it's important to take more care with the words you choose.
The "use it with friends and people you know well" rule is not exactly right either. I know many people who, despite being my friends, would just look at me strangely if I started speaking in a sloppy manner. The fact is, you have to pay attention to the other person and see if they actually use the slurred forms. If that person doesn't use them, you really shouldn't use them either when speaking to that person.
It helps to know about these words, but if you use them because you think it's "standard" or "real" English, native speakers will just think your English level is very, very low.
Mike is right. Don't use them. We find them really irritating.
The words you mentioned are often said that way but not as often written. The main reason you would want to write these words are to capture accurately someone's pronunciation such as when writing speech for a character in a story.
If you want to use words like these, then that's your choice, but as you can clearly see, some people are easily put off by it. I agree with Mike though that typing "u" instead of "your" or "ur" for "your" or "you're" really gives me the impression you don't care too much about your English so there is a good chance I would not bother mentioning any mistakes I spot.
Another thing which is common, which I ignore (other than to maybe remark on once) is when people always type "i" lowercase and not use punctuation. For me, I wouldn't think that that means you don't care about your English, just that you can't be bothered to type it properly.
If you used any words you mentioned, I wouldn't have a problem with it in terms of treating you seriously. However, the only ones I would ever use myself (other than for giving someone speech) are: "gonna", "wanna" and "kinda". I suggest you just stick with those if you know them well (and more importantly know when to use them) which I don't think you do as you only listed "wanna = want to" but not "want a".
Basically, you would be better off not using any of these words yourself. If you do use them, know them well and don't make it the norm.