I’m assuming she’s like Rosalina and Luma with the Egg Bot?

I've never played Rosalina but yeah pretty much.

Also the egg-bot's name is little Timmy

I’m assuming Phantom would work like a cross between Snake, Meta Knight, and Mii Swordfighter

I imagine that if you kill little Timmy that'll give Astra an attack boost instead of just summoning another one