How would you do things differently, Julius?
You are a logical man, yet you repeatedly ignored signs of detriment and danger for your own life--the soothsayer, and Calpurnia's dreams for instance. What was going through your mind at the time?
These will get you started. If you think about the play and possibly re-read some of the speeches, you will be able to come up with others. Imagine you are meeting him and interviewing him for a local paper or radio station.
Any questions you have about his motivation would be fantastic. Brutus makes much ado about his concern for the good of Rome under the assumption that Caesar is nothing more than a power hungry potential dictator. If you could get some honest answers from Caesar instead of political answers, it would have been interesting to hear his side of the story.
Historically, I've always wondered why he turned his back on Pompey and Crassus so quickly. That question has less to do with the play, but could help lead to information about his motivation, also.
I think you could come up with your own questions if you have a bit of guidance and re-read the play. You may want to gear your questions to his personal life - maybe questions about his relationship with his wife, Calpurnia; how he feels about the state of their infertile marriage. You might also want to ask him about how trustworthy he considers his friends to be, especially Brutus and Mark Antony.
Check out the link below, as well as all of the information about Julius Caesar available from eNotes. Good luck!