Of course you can import only the clips you want into another project.
When you first capture your video, you are given the option of selecting a general name for the series.
You can also rename the clips in Premiere Elements by right-clicking on each and selecting the option to rename.
And you can create folders in the Project media panel and store your clips in sub-sets there.
For the purpose of answering your questions, I am assuming that you are using Premiere Elements 7.
With your media in Project Media View, right click the file there, select Rename, and rename.
Right click the video on the Timeline, select Rename from the pop up, and rename.
If you have opened a project .prel and added media, that media should be incorported into the Organizer. Let us say that you open another (new) project .prel and want that specific media from that other project .prel. Look to "Filter by: Select Album" and under Select Album select that project in the list.
However, if you needed to transfer (use) your Timeline in another project prel, then save/export the Timeline (File Menu/Export/Movie as DV AVI. In that save/export, a copy is saved to the hard drive location of your choice as well as a copy being in the current project. You can then use the copy saved to the hard drive for use in other project prel via the programs Get Media/Files & Folders.