As an NES, but not a teacher:
1. I'd personally not use either.
1a) I don't believe just a pleasant smile would be appropriate.
1b) Unless she was wearing a clown costume or a big red nose etc I don't believe anyone would be laughing at her.
Maybe something like "great happiness" would be more appropriate.
2. A round of applause works for me.
3. I would replace the comma with a colon.
Hope this helps