If you want to edit images without having access to the originals (like when you disconnect your hard drive), you will need to have Smart Previews for those images.
If you've already imported all of your images or if you're using an upgraded catalog from LR4, then you may need to create the smart previews for the images that you want to edit offline.
The easiest way to do this is to go to the Library module, select the images or folders that you want to create Smart Previews for, then select Library > Previews > Build Smart Previews.
Once that process is done, you should be able to disconnect your hard drive and continue to edit your images, assmuning your catalog is on your mac and just the original images are on the external drive.
For the added question, I don't believe the Edit In (or Export) work with smart previews. The previews are stored inside a Lightroom specific file/directory, and the normal handshaking between Lightroom and other applications, including Photoshop, rely on the original, external file.
Hope that helps.
So I have to have both files, the "normal" "Lightroom 5 Catalog Previews" and the Smart Previews to be able to edit the pictures without connection to the EHD (correct me, if I did get it wrong).
What do I have to set up, that the normal "Lightroom 5 Catalog Previews" don't take up too much storage space? And is okay to work in lightroom?
You definitely need the smart previews to edit pictures without the connection to the EHD. If you just have the normal previews, you'll be able to see the preview, but you won't be able to edit in the Develop module.
Regular and smart previews are smaller than the original images, but if you have huge amounts of any sort of preview the file size will go up. If you're that concerned with disk space, then you can just do the smart previews for the folders or images that you want to edit while disconnected, and then delete the smart previews when you're done editing those images.
What I've been doing lately is having a "working" Lightroom catalog that has my active projects only. I keep that catalog on Dropbox so I can share it across machines, and since I only have the free account, I want to keep the file size of that catalog as small as possible. So new imports go in to this catalog with smart previews, I edit them, and when I'm done with that project, I migrate the project in to my "full" catalog without the smart previews. So my working catalog stays as small as possible, I get the benefits of smart previews, and I keep my footprint small.
Since I'm moving things in and out a lot, I optimize my catalog once a week just to make sure I'm not keeping a bunch of trash around.
In your catalog settings, you can also change the size of your previews and change how long you keep them. You can also discard all your 1:1 previews by selecting images/folders and selecting Library > Previews > Discard 1:1 Previews.
At some point, though, all the shuffling around might get to be too much work, so it may be worth looking at cleaning up disk usage elsewhere so you can find a nice balance.