मुझे गाँव नहीं आना है। can mean 'I must not come to the village', 'I do not have to come to the village' or 'I don't want to come to the village' depending on the context. The placement of नहीं after the infinitive just stresses the negation in either meaning.
If you want to avoid ambiguity, it's better to use different phrasing. Eg. मुझे गांव नहीं आना चाहिए (I should not come to the village).
Yes. However, keep in mind that पड़ना conveys a somewhat stronger (though less so than चाहिए) sentiment of requirement/necessity while the infinitive+है construction can convey anything between desire and obligation depending on the context. I'd say पड़ना is analogous to 'must'.