Las contracciones con 'd en su mayoría corresponden a "would" y nunca "should." Como mencionaste, 'd puede corresponder a "had" o "would" dependiendo del contexto. Por ejemplo: After I'd gone, they rented my room. = "After I had gone," ya que "After I would gone" no tiene sentido. La mejor manera de distinguir estas dos formas, es recordar que "would" siempre va seguido por un infinitivo, y "had" por una forma perfecta. Por tanto: I'd imagine = I would imagine; y I'd imagined = I had imagined. Espero que te ayude :)

Depende del contexto. Pero algunos son muy comunes. Por ejemplo: "I'd like a cup of coffee, please. I'd like a hamburger and a coke." = I would like (preference) "I'd better go now." = I had better (necessity) "I'd gone to the store." = I had + (past participle, e.g., "gone/seen/been/taken" (past perfect)