The first two (1) and (2) are correct. The third (3) is not correct.
1.How long have you been living in China ?
How long have you lived in China?
--> Both of these questions are asking the same question. So they have the same meaning. Maybe there is a nuance difference between the two questions, but most people would (i think) interpret the question the same way.
2. How long have you been learning English? --> 'learning' implies you are gaining knowledge of English
How long have you taught English? --> 'Taught' implies that you are giving knowledge of English to somebody else
Q:How long have you recovering from being ill? --> How long has your recovery been? = 'recovery' implies the hearer was sick/ill.
A:I have recovering being ill from thd last week . --> I have been recovering since last week = this is not the most natural way to say this = "A little over a week" or "Since last week". = because in everyday english/ conversation, you do not have to make a full sentence. You also don't have to repeat the exact same words.
I hope this helps :) if you have any further questions, feel free to ask