linking a requirement to a product or component

As you linked the requirement to a project, you only see products having versions linked to the project.
So you need to link versions to the project to see them in the list.
Note that since V5.5 you can directly link the product to the project, this will automatically link all its versions.
You can also chick the search icon (magnifying glass) beside the list to open full list and retreive the product you wish