AWS has a million services. One of those is S3, is that what you mean? S3 allows you to host a static website.
1) S3 works perfect for hosting my jekyll websites
2) no issues, even use cloudfront to get free ssl
3) bill will vary depending on traffic, my sites are pretty small, the bill for just S3 related stuff is less than $1/month for everything I have. I also use AWS Route 53 for DNS and that is probably more expensive than the actual hosting. I think it is $.50 per site.
4) I use the S3_website gem listed above, it takes some getting used to but it simple. It is command line driven just like jekyll so it can be confusing at first but it is pretty easy once you get the hang of it.