In general, for 1 and 2, a singular verb would be used.
Neither of us is more intelligent than she is
None of them lives around here
However, in speech and less formal writing, plural verbs are often used. To me ear, 'are' sounds utterly wrong in the first sentence, but 'live' sounds more natural in the second. If you are taking a test, it is probably better to err on the side of caution and use singular verbs.
For 3, it depends on the second noun. If the second noun is singular, use a singular verb. If it is plural, use a plural verb.
Source: Advanced Grammar in Use, Martin Hewings, 3rd ed 🙂