Hello, I would like to suggest that you include the limitations AWS Lambda and API Gateway has, since I have used them and it is not suitable for every use case.
For example, one of the biggest limitations is that an Lambda can run for at most 5 minutes, but if paired with API Gateway, it can only run for 1 minute before returning a time out, I know 1 minute is quite a lot, but if you have any kind of multimedia processing (like uploading a file, or downloading one that is generated on the server like a PDF) you will need to re write some code to use other amazon services such as S3.
Other limitations include things such as 100 concurrent requests at a time and 500 requests per second, payload for request and respose size limits of 6mb and other things that can be read here
http://docs.aws.amazon.com/general/latest/gr/aws_service_limits.htmlSome (most) of those limits can be increased by request to Amazon.
Leaving the limitations aside, AWS Lambda is really a great product I highly recommend!