I'm not sure of the best way to translate the original meme line while also keeping it suitable for tagging purposes. If anyone wants to take a crack at it, Pixiv has an entry on it here.
It's the handwritten form. The form you're more familiar with is used by computer fonts, but native writers don't actually write it that way.
They do too. Both forms are acceptable. Though the 1-stroke "z" form is standardized in elementary school teaching to avoid confusion among students. Likewise for teaching materials intended for Japanese-as-a-Second-Language learners.
The usual trend with these kinds of skits, would be that Ran becomes fiercly competetive over who is the better mother. A nice change of pace to have her essentially go "Haha, you are become baby." and continue to dote on Chen in peace. Plus, her smug face is endearing.