You may remember seeing Yuki's dad in strip 124.
actually, he has a first name. His full name is Sonada Masamichi. There just hasn't been an instance where he's been called by his first name yet.
The giant turtle sounds similar to Gamera, an old Japanese movie monster.
Bai bai = Bye bye
Yuki's mother might be a reference to Saint Tail. Saint Tail's name is Meimi and her love interest is an aspiring police officer.