I can answer most of your questions. Yes, it is possible to host an application with these technologies on AWS. You can host any application on the AWS server, just like any other server, but you must configure everything yourself, unless you use a configured AMI.
I would not recommend using AWS to send emails, however, as in my experience, many spammers abuse AWS, so if you send emails / etc ... from an AWS server, this can be handled more strictly by other spam filters email server. It’s best to use a third-party solution to send bulk email.
As for your last question: “how can I specify a domain to point to a web site hosted on AWS”, it is too complicated to answer here. I would suggest hiring someone who has experience with DNS to manage this transition. I would recommend that you move your DNS hosting to Amazon S3 Routing Service. You can then easily manage your DNS and other AWS services from a single console.
Good luck.
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