Q1 - 2
A doubt is a feeling. The sentence is about his feelings. It's not about things happening. Being sure is a feeling. He had doubt, now he is sure.
Q2 - no answer is correct.
I had doubts, in the past. What do I have now? The answers don't correspond to the question. Anthony's answer above makes sense.
Q3 - 1, but it's not a good explanation.
This usage usually means that we hope the outcome will be X but we're not confident that it will happen. We might get another outcome. The success is in doubt, really.
The explanation would be more appropriate if the question used "uncertain" instead of "in doubt."