No. It isn't. 'Don't' and 'I'm' and 'isn't', for example. are contractions that are also correct informal written English. 'Wanna' ( and 'gotta' and 'gonna') are NOT acceptable features of written language. Please do not believe anyone who tells you otherwise. Please don't think that 'wanna = want to' in the same way as 'Aren't = Are not'. This is not true. Then what is 'wanna'? It is feature of speech only. When native speakers say a sentence like 'I want to go' in a relaxed and fairly rapid way, it sounds like 'I wanna go'. We don't deliberately say 'wanna'. The words in our heads when we say this are 'I want to go'. 'Wanna' is not a word - it's just a sequence of syllables that occurs in connected speech. So why do we see the word 'wanna' written down? We write it down when we want to imitate speech. For example, if someone in a film screams 'I wanna be free!', then it's acceptable for this to appear in subtitles. Likewise, with song lyrics, or cartoon captions. Or maybe in a short text to a friend, when you want to be funny and friendly. But that's all. Many non-native learners of English believe that if they write 'wanna' in all their sentences, their English will look 'cool' and informal and natural. It doesn't. Browse a little on this site. See who writes 'wanna'. You'll see that it is only non-native learners. Don't copy them. Write proper English.

"Wanna" is NEVER written except in transcriptions of speech (subtitles, song lyrics, direct quotes etc.). Don't make the mistake of thinking that "wanna" is simply a slang word that native speakers consciously use in an informal situation. "Wanna" is just how "want to" or "want a" come out when speaking very quickly. Normally what's actually said is somewhere in between e.g. "wanta" or "wann-oo". It just rolls off the tongue quicker. People don't say it consiously, and if you put any kind of emphasis on it it will sound unnatural. If you ever write it, it will be obvious you're not a native speaker. A lot of learners think that writing it will make their English seem more natural or informal; it won't. Even in the most informal contexts, native speakers don't write it. Like I said before, the only exceptions are in transcriptions of speech.

Yes. It's "want to" in american slang.