I realize this was posted a few weeks ago, but some comments from my own experiences.
Depending on the program you want to apply to, you DO have to apply by a certain date. As jessi22 stated, that opening page will tell you the dates for specific programs.
That being said, the do offer invites and interviews on a rolling basis, so the earlier you apply the better off you would possibly be. THAT being said, it is still very possible that you could apply right when a position opens, but not hear anything up until just before the know-by date after you've been put under consideration; at the same time you are hearing of people being interviewed and/or invited for the same country. It really is a 'depends' kind of application process and your mileage may vary greatly.
Jessi's (assuming it's Jessi!) suggestion about contacting a recruiter is probably the best advice a prospective applicant can get - they can really help you tailor your resume and let you know what they are looking for for certain programs.
As for all the other questions - it really is a matter of depends (get used to hearing that!). Some people in my staging group found out only a few months after applying, others didn't find out anything until literally the know-by date. You are pretty much guaranteed to have four months between the know-by date and the staging date if you do get invited...but that is a busy four months, with medical, dental, etc. having to be done (I think it's four months...might be slightly more or less). Due to various reasons, the process itself can also vary, but under today's process, usually takes no more than a year. Medical issues after invitation can bump that up (for me, it will be two years until I leave), but in general, if you get cleared to go to your initial invitation, then about a year at most (as a result of them posting positions a year ahead of time).