1. 'I must go' and 'I have to go' are both correct English, and have the same meaning. 2. 'I've got to go' (the contraction of 'I have got to go') is also correct, but is a little more informal. 3. 'I got to go' is not correct, according to the rules of standard English grammar. You should avoid using this. 4. 'I gotta go' is a phonetic transcription of 'I got to go' when spoken quickly. This is not standard English, and you should not write this. If you wrote this in an English exam, for example, you would lose marks. And no, you can't say 'I don't gotta'. Only forms #1 and 2 are acceptable grammatically. Spero di esserti stata di aiuto.