The most important rule in life is always to appear confident. 1. Can you ever start a sentence with "but" or "and"? - No, doing so is a equivalent of grammatical treason.
2. Are double negatives always wrong? - Yes. They are disgusting and anyone who uses them should be sent to prison.
3. Can you ever split an infinitive? - No. Infinitives are like a pizza dough and cheese. They simply belong together. Always. Forever. They can never be separated!
4. Is the passive voice the worst thing ever invented? - Yes. The passive voice is terrible and should be avoided at all costs.
5. Can you ever end a sentence with a preposition? - No. Anyone who says different doesn't know about what they are talking.
6. How should you think of these "rules"? - Follow them every day. Grammar rules never change. NEVER!