Yes it does make sense. The teachers on this board are happy to help you, and MFPA is a great choice of materials (the best, in my opinion) for any teacher of young ones, experienced or newbie. Be sure to watch all of Nancy's videos! And somewhere is Randall's explanation of what motivates children at each stage of their development. Age 5=fun, later=independence, etc. Someone, help? Links? Can't find it at the moment.
If you can catch one of their workshops, that would be fantastic too.
Related to your first question, how long to stay on a piece, keep going back to previous pieces. You could call them "just for fun" pieces, or AAA pieces (child's favorites, memorized, so they're playable Anywhere, Anytime, for Anybody). Some pieces are OK to check off when they're pretty good, others you will want your child to get nearly perfect, with consistent mostly correct notes, good hand position, nice dynamics (well, I guess you pretty much want that for all of them

). Sometimes you will move along through the pieces, other times you will stay on a set of pieces for awhile. Just enjoy that--it isn't "getting stuck," it's letting things sink in.