1 - The RDS service automatically manages failing machines and moves your data to a new machine with the same name so it looks like nothing happened. This is part of the service you're paying for when you use AWS RDS instead of just installing your database of choice inside a regular EC2 instance.
That having been said, you may want to look into Multi-Availability Zone deployment for your DB instances, which runs and updates a passive copy of the database so there is less interruption of service while automatic repairs occur. It basically costs double.
By default, RDS instances automatically take daily backups and keep running logs so you can restore your data to any point in time within your retention period. I think the default retention period is 1 day, but you can set it up to 35 days.
You can also create manual snapshots of your database at any time that do not expire. The snapshots are stored in S3 until you delete them, and you pay only S3 storage costs to maintain them.
2 - I'm less familiar with Beanstalk services, but I believe there are ways not to lose the data. One idea is that you can configure a database instance to take a final snapshot when the instance is deleted. Then, when the whole Beanstalk deletes, the database data should be safely stored in S3.
Another idea would be to just manually take a snapshot while your Beanstalk is still running.
Hope that helps,