- For most verbs this is syntactic: the verb do is added (properly conjugated) and followed by not (generally contracted) followed by the verb. A select number of verbs allow not alone to form their negations (be, have, will, etc.) and these are also generally contracted.
- It depends on what you include in your pairing of opposites; but that is a philosophical question, not a linguistic one.
- English doesn't mark verbal negation morphologically; the prefixing you are describing is derivational affixing, while the formation of negatives would be inflectional (and something English doesn't have for verbs).