Preface: annotations are something different, what you're talking about are called DocBlocks.
PhpStorm automatically resolves parameters
Not in my experience; if you're using the namespace at the top of that file
then yes, just like in the rest of your PHP code in the same file, you don't need to use the fully qualified namespace when referring to that class.
use statement at the top of the file, PhpStorm won't be able to resolve the class (without the differentiator of namespace, how would it distinguish between two identically named classes?). At that point you'll probably see a squiggly line under the class in the docblock, informing you that it couldn't be found.