First off, welcome.
Second, those questions are slighty slower than "quick" for my standards.
Anyway, her jab is best to repeatedly jab cancel or, if you are spaced safely so that Luma will hit the opponent's shield but not Rosalina's, three hit jab. This pressure can lead to various opportunities depending on you opponent's choice.
Rosalina has in fact trouble against juggling, she has a slower air speed than Peach, for that matter, so you need to mix movement and airdodges to not let your opponent catch you.
When approaching, you can beat the shield by boost grabbing, Lunar Landing and spacing Luma.
You can beat an attack by using the Nair advancing during the initial part and retreating during the second, depending on the attack, you can also run and shield the attack.
You can beat a grab with the Nair, but unlike before, you can as well hit your opponent. Well, most attacks beat the majority of the grabs, for that matter. You can also preempitively imput an attack so that Luma will free you once grabbed. Take note however that you can do it only if Luma doesn't get hit by eventuals pummels and throws.
Fox's lasers are unsafe at closer distances, where firing them usually results in Fox being hit before the endlag ends.
At longer ranges, just spam gravitational pull, though be ready for an approach from the enemy. Also if you crouch Luma will dodge the projectiles, from that point any action that holds Luma in place such as powershielding and using the majority of the moves will result in Luma stopping in that spot without returning to the normal position, basically the same concept of maintaining the position of a launched out Luma.
Coffee Fish can indeed hit Luma if Rosalina hits him, as such, you must actually move out of the move's hitbox.
