I included other speech acts. Thank you.
1)“How would you like to go to the zoo?”, he said. “I’d love/like to”. “That sounds great”.
2)“Would you like to go to the zoo?”/”Do you want to go to the zoo?” “I’d love to, but I can’t”.
3)“I’m organizing a party for my wife’s birthday. Do you think you can/will be able to come? / Can you come? Can you make it?”
1-3) He invited me to go the zoo. He said he was organizing a party for his wife’s birthday and invited me to go (not come). I accepted/refused to go to the zoo.
4) “I’m sorry, I’m late.”/ “I apologize/I’m sorry for being late.” “ Forgive me for being late.”
“I’d like to apologize for being late”, she said.
5) She apologized for being late.
In 1 and 2, the ending periods belong before the closing quotation marks because those are full sentences:
... "I'd like to." "That sounds great." etc.
Also with the comma after "late" in #4.
Everything else looks fine.