I am concerned that photos can be copied from this site. Is there a way to prevent that?
Not really. Anything that can be seen on a screen can always be copied by someone who is determined to do so. The best way to protect your images is to only post smallish, low resolution versions that would not have any commercial value. Dgrin itself does not have the capability to limit resolution, but most photo hosting sites (like SmugMug) let you limit what the public can see. Most people here embed links rather than attach images. If you don't use a photo hosting site, you should lower the resolution before uploading to Dgrin. Watermarking your images can also help, though you might get some bitchy comments from people about how the watermark makes it hard to appreciate the image. Also, there are increasingly sophisticated technical means of erasing watermarks, so you shouldn't only rely on them.
Yes, don't post you photos online.