Triton terrified her to death I think she would have ran away with or without Ursula's help

i don't think so, she really love her familly according to what she said to Ursula, and without Ursula i think she might have be ran of ideas.

I should think so.

She may have stayed in the grotto that night, but I highly doubt she would've run away completely.

her father was so strict! and ariel was fond of the outside world.

She would still be mad at her dad and would ignore everything he said to her. Or like firegirl1515 said, would stayed away 2 or 3 days.

Not at that point, No.
Eventually, Yes.