Hi
You can apply for medicine as well as other post-graduate courses at the same time. Doing so won't impact the outcome of the offers (many people will receive multiple course offers). Applications usually open around late September/ early October and may close around December (some courses, which may be less popular, may be open until just before the start date of the course). Most courses (unless those that are highly competitive) will also give you a substantial amount of time to think about the offer before you need to accept it. This information can usually be found in the subject/course guides, so I highly recommend looking at them if you want to know when applications open and close.
Next year (and maybe even in semester 2 this year), subject coordinators will make announcements of upcoming postgraduate information sessions, where course-specific information will be explained and you can ask questions.