Now with the MyEclipse Deployment tool will it only synchronize the project deployment directory and the application server deployment directory when that instance of the server is started and running?
It keeps them synchronized all the time, wether the app server is running or not.
Can I have multiple server deployments setup for one project? So I could have a deployment setup for Resin and another one setup for JBoss?
Sure. When you click the DEployment tool, select the project you want to deploy, hit Add, and then add any number of deployments to any number of servers you want.