You will have to pay for Europe as a fifth continent whether you stop there or just transit on your way from Asia to North America.

YYZ-ORD-YYC counts as two segments, so it all depends on what your other North America segments are, you are allowed a total of six. If I remember correctly you are also limited to two stops in your continent of origin which may pose a problem for your desired itinerary.

I doubt very much they will let you go over the one-year limit.

About AAdvantage miles for a OWE RTW in coach, you need to be careful with BA (no miles for transatlantic, possibly no miles at all depending on your country of residence), CX (no miles unless you have a Canadian address), EI (no miles), IB (at best 30% miles), and QF (70% miles). Try to book as many code shares as possible on AA, AY, or LA code (must be oneworld metal) as they all earn full miles. This is from memory, I may remember wrong or it may have changed. You can read about the current rules at aa.com/memberguide under Earning miles.