Any way to get IntelliJ-like autocompletion in Eclipse?

Go to Window → Preferences → Java → Editor → Content Assist. In the column "Auto activation triggers for Java", enter this:

.qwertyuioplkjhgfdsazxcvbnm_QWERTYUIOPLKJHGFDSAZXCVBNM

Add any other keys you want. You're done. That answers your first query. As far as second one goes, I think it already exists.

I have to say NO. I moved from Eclipse to IntelliJ because of the intellisense and inability to make Eclipse behave like IntelliJ (or if you come from the .NET environment: inability to make Eclipse intellisense behave like ReSharper in .NET).

Do you HAVE TO work in Eclipse? I do 98% of work in IntelliJ, then convert the project into Eclipse project (IntelliJ can still access it) and finish it in Eclipse. Maybe you could try this solution.

Take a look at Eclipse Code Recommenders [1] or Codetrails Connect [2]. They make Eclipse' code completion intelligent.

[1] http://eclipse.org/recommenders/

[2] http://marketplace.eclipse.org/content/codetrails-connect-community-edition/