Everyone is saying the revolving arrows are 100% RNG, but I found that if your n#1 squad is facing an arrow and you align it with the direction you want them to take when pressing the next button they always go in the right direction. You can also try calculating the distance and time it will take other units to pass through the arrow at the moment they're pointing the right direction, though the margin of error seems to be quite large.
So, from my personal experience, I'd say the arrows are not random if the units pass through them when they're pointed directly at a path. Am I wrong? D:
Farming Manyus is essential for leveling your girls, but 100%ing stages is great for farming flower gems, so it really depends on your priorities. I finished completing all stages just last week(I've been playing since day 1) because at times I did take my time farming for manyus and mats. it's your call, really. I don't feel like there's a right answer.
Edit: I do agree with not rushing the 3 medals on the dragon missions, though. Try doing that only when you're about to evolve a girl and need the mats. Btw, get the girl to cap lvl before trying to farm the lvl100 dragons