Advantages of using the Amazon RDS:
They manage it for you (back-ups, mirroring, etc)
Biggest Disadvantage for using the Amazon RDS:
The potential cost of having them run the server for you 24/7.
If you have the money for the added cost of them managing a MySQL server for you then I would say go for it. If you feel comfortable with managing a MySQL server and you can wrap everything onto one EC2 (possibly problematic) it would be cost effective to do it this way. Alternatively, look into the Simple DB system and see if it works for you. If you have no need for a full relation DB system and seeing relatively light DB load it may be advantageous.
If your loadbalancer fails, it can be really crappy. In all likelihood you will lose the assigned address. But the loadbalancer "should" come back by itself. However, I have heard of people having a load balancer running under load for over a year without problem.
There are quite a few tutorials out there on how to setup a webserver up as a proxy/loadbalancer.
Effective use of the EBS depends on the specifics of your application. EBS volumes are easy and quick to create/mount/dispose of. You can create and mount them dynamically. There are SDKs for manipulating most every element of AWS written in pretty much every common language. Personally, I am using the AWS SDK for PHP and it works very well. There are also a number of command line utilities to use with shell scripts.
http://docs.amazonwebservices.com/AWSSDKforPHP/latest/index.html is the documentation for that. Otherwise, look through the AWS Developer tools for other languages/utilities.