1. What are you going to do for Chuseok?

I am going to buy some gifts tonight and I will hand them to my cousins on/for Chuseok.

(Can we use 'for' in Sentence 1 before Chuseok?)

2. What are you going to do on Chuseok?
Three days ago, I bought some gifts for chuseok, so I will give them to my cousins on/for Chuseok.

(Can we use 'for' in #2 before Chuseok?)

Yes, you can use 'for' in both sentences. You can also use 'on' if the answer will be about activities that will take place on that day.