Uhms... I don't really have much advice that is tested and proven. But I guess do your best for MCAT and get a good GPA.
You'll need around 3 recommendation letters... so the best people to get it from are your professors, your boss, and if you've done clinical shadowing etc, the consultant. This will take time. So start collecting as soon as possible.
As for the application essays, it is a good time to market yourself. Think along the lines of job interviews: how would you add to the profession, why should they pick you and how would you fit in. Good time to review what is the medical school you're applying for is all about.
Extra curricula can gain you an additional advantage. Research experience and medicine related volunteer activities are a plus plus. I guess publications in medical research are big big bonuses.
If all things goes well, you'll find an email one day that invites you to applicant day and you know you're halfway there! If you're local, it is best to know a little about the Singapore healthcare system and what are the problems that we face. If you have time, you can pop by the SGH museum, read up SMC's annual publications. Familiarize yourself with what the profession is all about, there are plenty of biographies written by doctors all over the world, couldn't hurt to grab one and read for leisure. Some can be quite entertaining! And above all, know what you wrote for your application. Wouldn't look good to go in and unable to answer what your honors research project was about. Above all, RELAX.
After that it is all about the wait, staying sane while keeping your fingers crossed.
Good luck and all the best. And may you receive that offer letter through email! (check that spam/junk box)