If you can outline what you did wrong during the checkrides, how you corrected the problem(s) and what you've learned from your mistakes, you have a chance. They'll ask you about failed checkrides for sure. They aren't asking to find out if you've ever failed a checkride, like the question itself. They are asking you to elaborate on how you succeed during hard times. I don't think it's a good idea to leave it at- you failed out of nervousness. State what you did wrong and what you did different to pass. Very few pilots make it an entire career with little difficulty.
Suspended license- state why and what you did to correct and get it reinstated, whether it be a fee and waiting or paperwork etc...just don't give them a reason to believe that you still deserve a suspended license
Speeding ticket- alot of people get speeding tickets and in my personal opinion, interviewers bring up one mere speeding ticket to judge your reaction to the inquiry. Some interviewers ask and some don't. Hey, if you made it to that part of the interview, think about why they ask the question, not merely the fact that they asked it. If they hire you, they're gonna put you in an airplane and they want to know how you're going to handle FARs and SOPs. It's up to you to explain the ticket.