Answer:  There are many ways to identify a mentor. View all the Summer Opportunities. Talk to students from previous years. Talk to your society advisor. Talk to Dr. Stanford. But it really comes down to your career goals and interests. This is a great opportunity to learn about future opportunities, and also to build your CV so that you are better prepared to match to a particular program. 

Answer:  If you would like to advertise your summer research project opportunity, fill out the new "Investigators Seeking Research Trainees" section in Faculty Activity Collaboration Tool (FACT). You may also make arrangements with students individually

Maybe. Some internal and external training programs have paid, short-term research slots for medical students. In addition, your mentor may pay you. If you do not secure a paid project you are still eligible for financial aid since this is a course you will take for credit.