We actually did FL on our trip a few weeks ago on a regular, non MM morning. It was our first day at the parks, and I figured best to do it first and then we could do it again on our MM if we so chose. The crowd at rope drop pretty much split in half - those off to do Nemo, and those heading straight to FL! We stopped off for FP's for Buzz, and dh got lost on the way (he was supposed to get in line for PP and I would catch up....), so even losing those few minutes, we did the following...
Park open @ 10
PP - 7 minute wait
Dumbo - waited one round (Ride was running when we lined up, and we were next on...)
Mr Toad
Carousel (dh and ds rode Matterhorn)
We missed Alice, as it was broken down, so we headed to TL to try and meet Buzz at 11pm.
So we did half of FL on a non MM day with little to no waits. By the time we left FL @ 10:50, there was still hardly any wait for Pinnochio or Snow White (too scary for my ds!), but lines for Dumbo, PP and Alice (when they fixed it) were pretty long. Storybook Land boats line was INSANELY long, however it still seemed to move pretty fast, as did the Casey Jr line.
Not sure about FL during parade times - we kind of avoided FL like the plague during the afternoons, since it was busy and congested. Someone else can probably help you, though!