2. Does the Coast Guard select officers right after graduating college?
According to the official website links, yes. You can apply as a senior in college if these criteria are met:
Baccalaureate degree will be conferred prior to the first OCS course convening for which the panel is making selections.
The applicant provides an official letter from their college registrar certifying their enrollment, degree, major, GPA, and anticipated date of graduation.
3. What can a college student do to improve their chances for OCS?
The same as any high school student apply to a SA, SMC, or ROTC - exceed academically, demonstrate an ability to juggle multiple responsibilities, volunteer, participate and lead extracurricular activities, maintain your physical fitness. The links above show you the minimum standards for all the application areas - so work on strengthening those. I would also add that you should demonstrate an interest, engage with recruiting (don't let them talk you into enlisting unless that's what you want), see if they can organize (or better yet - if you can organize) a visit to any local Coast Guard units. I've sat on a couple of OCS interview panels. When/if you get to that stage, make sure you can clearly communicate why you want to commission as an officer and what YOU can bring to the Coast Guard.
This is a little dated but the Coast Guard created an Officer Application Job Aid Kit - this is the 2014 version, I wasn't able to find the 2016 version online (which is the most up to date I believe). It speaks to the stats you were looking for and what the Coast Guard is looking for in your application package: