Yes, many classes transfer to the University of Alberta. It is important to attend an advising session to clearly identify those classes that do transfer to your destination University and plan our course load effectively. You can also check the transfer uide to determine which courses transfer from Mount Royal to the University of Alberta.
Yes it is important to know which courses act as prerequisites for others. The advising sessions give you an opportunity to interact face to face with an advisor who can help you with all your planning and concerns.
Currently the Department of Education at the University of Lethbridge will accept transfer students without Math 30 though this does not hold true for either the University of Calgary or the University of Alberta. Questions like this are discussed in advising sessions that you are encouraged to attend.