Let's get started on the Rosalina and Captain falcon MU.
:Rosalina can give falcon a hard time appoarching since he doesn't have a projectile. There's her forward and down-tile, star bits, and n-air to stop him from coming in on her. Since Falcon is a large target, she can combo him with her up-throw and down throw at early percents along with a couple of up airs since he can't get out of her strings due to falling speed and being heavy. If she gets falcon above her in the air, then she can juggle him with her deadly up-airs and maybe kill him off the screen with luma(depending on damage and rage).
While falcon's edgeguarding game is slighty stronger, she can also gimp falcon's recovery with d-air and back air. You can also use luma to cover falcon's get-up and roll with Rosalina to down smash, down tile, grab, forward tile, or forward smash.
:Falcon has the moves to knock Luma off stage such as dash attack, forward smash, falcon kick, knee(if you want to be brutal), and down smash. Some of his moves can also separate Rosalina and Luma because they have enough knockback to do so. Once Luma is gone, this is your chance to rushdown Rosalina.
His damage output is better than Rosalina so his combos will work on her since she's a large target. His Ko potential is better and also, he can kill Rosalina early than she can because she's light. Rage benefits Falcon more than Rosalina since he's heavy and can take more punishment than she can. Falcon's mobility both in the ground and air are better for him to juggle her, land better(his falling speed is fast), combo her, and catch up to her if he knocks her off stage.
Falcon's edgeguarding game is sightly stronger than Rosalina's because even though Rosalina's recovery can reach the ledge more than falcon, it doesn't have a hitbox and it's predictable like Falcon's. His d-air, the knee, and back air can take Rosalina out early depending which angle she uses for her recovery. Also if she grab the ledge twice, then this is the perfect time to use falcon's up-tile to spike her down(if spaced correctly with the foot).
Stages: Final destruction, its easiler for Captain Falcon to appoarch Rosalina with no platforms around; However on Battlefield and Dreamland, not only she can make it alittle harder for Falcon to appoarch and keep luma safe with platforms, but can also juggle falcon with up-tile, up air, and n-air because of her being tall.
Customs:
:Falcon dive without the grab can make it difficult for Rosalina to gimp him unless she's lucky with well timed down air before he grabs the ledge. As long as he don't grab the ledge twice which means for a down air, back air, and maybe down tile, he'll be fine.
:With shooting star bit and teleport luma, she can level up the playing the field. Shooting star bit can use to stop falcon's appoarches, bait rolls or air dodges to punish, and as a projectile.
For the Mu, I say its 0(or even) because while Rosalina has the tools to edgeguard, stop appoarches, and range to bring down the Captain himself, Falcon has the mobility and power to take out luma and rushdown Rosalina. Customs, I say 0 or 0.5+ slighty in Rosalina's favor because with Shooting star bit and teleport luma, it steps up her game with edgeguarding and to stop falcon's appoarches even more with shooting bit. Keep your luma safe, and good luck destroying falcon together.