>>I was just wondering if there are search engines on the internet who take exactly the same search results as shown by the search index of ODP.
If I understand your question correctly, the answer is NO! ABSOLUTELY NOT! NEVER!
The ODP search index is little more than a COMPLETELY-un-page-ranked-or-relevancy-tested COMPLETELY-random-order search of the ODP SITE, including all of its listings of website titles, descriptions, and URLs. No post-stone-age real search engine would limit itself to no-relevancy-order-whatever and less-than-3-million-pages-listed!
You can, if you wish, put a link to ODP search on your own site; many editors and a few other people have done this. You can, if you're moderately clever, get a great deal of good information starting from ODP search and browsing ODP categories. But it is not and will never be mistaken as an adequate substitution for a search engine.
Every now and then someone gets excited about their alleged high "site rank" in ODP, or tries to figure out how to improve their low rank. It's a waste of time for both reasons mentioned -- there is no rank, sites appear in an order that has NOTHING whatsoever to do with ANYTHING at the site itself, or the frequency or relevancy of ANYTHING in the ODP listing. There are only two ranks for ODP keyword searches: 0="not found" and 1="found".