Free tier limit exceeded

Hello.

The sentences listed there will be written if even one EC2 instance is started.
To check whether you have actually exceeded the free tier of EC2 instances, you can check by following the steps in the document below, or by looking at the "Offer usage" graph in the image.
https://docs.aws.amazon.com/awsaccountbilling/latest/aboutv2/tracking-free-tier-usage.html

Looking at the graph in your image, it looks like the free limit has not been exceeded.
If you are concerned, it is a good idea to display the global view from the URL below and check if EC2 is located in another region.
https://us-east-1.console.aws.amazon.com/ec2globalview/home?region=us-east-1#

I'm using the aws ec2 instance but sometimes it sleeps because of the 'free tier limit exceeded'. how can I fix this?

By the way, does sleeping mean that the EC2 instance stops working?

how can I remove the free tier without terminating my instances?

If you start even one EC2 instance eligible for the free tier, the free tier will be consumed, so you need to delete EC2 to stop the free tier.
https://aws.amazon.com/free/?nc1=h_ls&all-free-tier.sort-by=item.additionalFields.SortRank&all-free-tier.sort-order=asc&awsf.Free%20Tier%20Types=*all&awsf.Free%20Tier%20Categories=*all

From your screenshots it looks like it's Storage space on EBS that is forecast to exceed the Free Tier limits - today is the 2nd of the month but you have already used up 14% of the month's Free Tier allocation.

The Free Tier allocation for EBS is described at https://aws.amazon.com/ebs/pricing/

AWS Free Tier includes 30 GB of storage, 2 million I/Os, and 1 GB of snapshot storage with Amazon Elastic Block Store (EBS).

30GB per month means 30GB can be allocated at midnight on the 1st of the month, and remain in place until 23:59 on the last day of the month, and it will not be chargeable.

If you allocate (say) 60GB on the 1st it will breach the Free Tier limit by halfway through the month.

You should also be aware that if you stop an EC2 instance then the clock stops on the EC2 Free Tier usage, but not on the EBS portion. As long as the EBS volume exists, whether it is attached to a running instance or not, it still gets counted towards Free Tier.