I already stop lightsail service, but AWS issued the bills

Hello.

Lightsail instances should still incur charges even if they are stopped.
You must delete it to stop incurring charges.
https://aws.amazon.com/lightsail/faq/?nc1=h_ls

Q: When am I getting charged for a plan?

Your Lightsail instances are charged only when they're in the running or stopped state. If you delete your Lightsail instance before the end of the month, we only charge you a prorated cost, based on the total number of hours that you used your Lightsail instance. For example, if you use the least expensive Lightsail plan for 100 hours in a month, you will be charged 47 cents (100*0.0047).

If you want to delete it, please check the document below.
https://lightsail.aws.amazon.com/ls/docs/en_us/articles/delete-an-amazon-lightsail-instance

1. How to cancel the bill and refund it?

If you wish to dispute your AWS bill, please open a case with AWS Support under "Account and billing".
https://docs.aws.amazon.com/awssupport/latest/user/case-management.html

2. I don't know how to get the stop date infomation, I only captured the stop status today, but I can't find out the stop start date information. here with I attached the captured image.

If it is within 3 months, you may be able to check the suspension API etc. from the CloudTrail event history.
https://docs.aws.amazon.com/awscloudtrail/latest/userguide/view-cloudtrail-events.html