It was banter. It wasn't a bad thing that she did.
You can get married at 16 with a parents permission. Or 18 otherwise. But that's just the modern way. It is probably lower in Suckloft and Hyrule due to the shorter lifespans of its people.
He shows affection because the focus is on them. Its...
It was playful banter. Nothing wrong with pushing him off cliffs.
And link is not too young for a relationship with Zelda. They are 18 or at least 17 which is old enough to get married at.
Link has always been feminine.