1. is there package tour that can bring you to most tourist spot in Xiamen in one day?

In my opinion, it is not suggested to travel with tour agency in that city and one day is not enough for the city.
South Putuo Temple, Xiamen University and Gulangyu Island are highly recommended for you. If you can, you can spend three to four days there.
It takes around 8 to 9 hours on the way and the ticket fare is 330RMB for second class seat and 406RMB for the first class seat. Or you can find more train information on https://www.travelchinaguide.com/china-trains/.