@Jman I think you need to understand power bi embedded fully to be able to make decision but below are the answers to your question with some more information on power bi embedded.
1. Using power bi embedded you can integrate power bi visuals in your web app but someone has to build that visuals first. so yes they can see their own data in your web app but someone would require to buid those reports / dashboards using customers data first.
2. Ability to drag and drop to create own reports is only available via power bi service. Power bi embedded is purely for integrating created visuals into web app.
3. I am not 100% sure but i think currently from power bi you can't connect straight to AWS database. I know there are number of Ideas posted regarding this including for Redshift and some of them are under review or started. You can also potentially research and test on ways to connect to that data source in AWS such as import it locally somewhere and then use in Power BI.