Someone can easily block you from using S3 static website hosting by adding a bucket with your domain name before you do. Also if you delete a bucket and do not change your DNS, someone can recreate the bucket and will be serving files from your domain.
This way you are not limited by bucket names and you also avoid any SSL validation errors.
Note: you can set Cloudfront's TTL to 0 if you don't need any caching.
However you are going to pay for Cloudfront requests in addition to S3's. In the vast majority of cases, it's insignificant compared to the savings you can achieve on the bandwidth side. (And at a certain level you can ask AWS to waive CF request fees entirely).
That's not correct. The S3 bucket name is always prefixed. The format is: bucketname.region.amazonaws.com.
https://docs.aws.amazon.com/AmazonS3/latest/dev/WebsiteHosti...
To clarify, you're going to have to add a DNS record either way. Doesn't matter what you call your bucket. And no, you don't need to put CloudFlare in front of it for this.