Q:

Negation of verb/gerund

I made up the following sentences. Which version is correct?  

 I prefer being by myself and not depend on others. 
I prefer being by myself and don't depend on others.  
I prefer being by myself and not depending on others.  

The first version looks to me a nice version to hear it. But negation of the verb seems to me wrong.  
The senond one looks pretty grammatical.Due to we negate a verb with auxiliary verb do 
The third one uses gerund. It doesn't nice to hear. But it make sense because it combines the sentence in a good structure: Subject+Verb(Gerund + Gerund)

A:

The first sentence is wrong because "not" can't modify the following "depend". The second and third sentences are grammatically correct but have slightly different meaning. 
Sentence 2 describes what I do (I don't depend on others) while sentence 3 describes what I prefer (I prefer not depending on others).

