<-it can be used while grabbed too
I think this is apart of her forward special, see below.
Forward Special
<- Maybe this is the Luma's forward special?
Sakurai said in yesterday's pic of the day the Luma can be "close to Rosalina or set further apart." I think her side special is exactly what this does. In the trailer, Luma never went to Rosalina unless she did an action which had to be this move to call it back.
In the gif where Rosalina and Luma tag team to hit Pit, you can see this is what happens. Rosalina uses this move to set Luma apart. Luma stays faraway from Rosalina, copying her moves, not going back to her (UNlike Nana).
In the gif where a red Luma shoots Star Bits, she also uses this move, does another action to make Luma use Star Bits, and then Luma goes back to her presumably using this move. You can see this happen when DK has Rosalina grabbed and the same effect from the red Luma also appears on the green Luma suggesting this is the case; Rosalina pressed Side-B while grabbed to do it.
Neutral Special when a Luma is active
<- Yellow
<- No idea what this is, but she's only waving her wand
<- Red
<- Green?
Now, see, this doesn't make any sense if you think about it. All the colored Lumas do the same attacks with seemingly the same properties. That's why I think the color is random when they're summoned. Claiming that they act differently causes more irrational speculation.
@Green Luma: This is the only instance we see Luma using an aerial attack, this happens to be a down aerial. Rosalina used down-A while grabbed to do it.
I think when Luma is active, Rosalina can make Luma shoot Star Bits because I can't think of anything else. Luma is just standing, and doesn't look like it can be an up tilt or down tilt, we've already seen Rosalina's/Luma's up/forward/down smashes. So this is either a forward tilt or neutral special while Luma is active.
This is her forward air, the angle isn't high enough to be an up air. We haven't seen her neutral, up and back aerials yet.
I'm not entirely sure this is her taunt. It's the exact same animation as her Luma summoning. I think this is just her using it when the Luma is active so nothing happens except her animation. Or Sakurai just decided to use that animation as a taunt too, who knows.
Considering how fast the gameplay was here, I'm not entirely sure it's Luma's taunt. It could just be an idle animation.
Oh nevermind, lol. I rewatched the video. This is certainly Luma's taunt.
???
<- Maybe forward tilt?
And I have no idea what this is, lol. I think it's a dash attack basing on how fast Luma is going but meh.
If I didn't explain my thoughts on your other speculations, then I agree with you.
That's unusually strong for a jab combo. I wonder if it's something else.
Let's not forget about Snake and Ike's jab in Brawl. Also Mario (and Luigi especially) have already taken damage clearly. The animation also matches a few other instances in the trailer where Rosalina does this jab and Luma does some punches.