Whether or not RMQ is a worthy topic for this project is not a question that we can really answer. We have not participated in your entire course, don't know what you have or have not covered. We don't have the project description (nor do we really want it). These questions you have posed would be good questions for your professor and this is a project that should be done by you, not a community.
All of the tutorials on Topcoder (your link is broken) have links to problems from the different judges that use the ideas in the tutorials so that you can attempt them.
If you need help and can show that you're doing the work and don't understand something, then by all means, ask for help, but make an attempt yourself first.
