EL methods with parameters
This is a bug of Eclipse WTP JST Tools. You can disable Eclipse facet validator in Windows->Preferences->Validation->Facelet HTML Validator.
Annotated managed beans
Unfortunately, JBoss Tools still doesn't support annotated managed beans. See https://issues.jboss.org/browse/JBIDE-5045
Implicit EL Objects
JBoss Tools doesn't provides code completion (and navigation) for implicit EL objects. This functionality came from Eclipse WTP JSF Tools. And I agree that it has mentioned bugs. Anyway please feel free to create a feature request in https://issues.jboss.org/browse/JBIDE against JBoss Tools. It seems that we should start covering this too to avoid WTP's bugs.
Duplicate tag suggestions
Looks like a bug but I can't reproduce it. Could you create an issue in JIRA and describe the steps to reproduce it.
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Thank you for the feedback!