There are two questions here. Firstly, can you extract a subset of a CC BY-NC-ND 3.0 database and distribute it on the web, and secondly, can you use that subset to inform the decisions of a piece of software with which others interact. You have the added complication that you're asking about the German language version of the licence; I'm assuming that it is, as CC say, a mere translation of the English version, which is the only one I can speak to. I'm also assuming that the database is a collection of facts, and not (eg) poems, or some other content in which copyright vested before they were so collected.
Regarding the question of subset distribution, as unor points out we already have an answer about excerpting *-ND works, which argues that you may not. But that question is specifically about creative works, whilst in this case the work is a database, and different jurisdictions recognise different amounts of protection for databases. Some, notably in the EU, recognise a specific database right; others say that copyright protection can arise through the originality implicit in its creation, but the extent of this depends on how the database was assembled, of which you tell us nothing; still others say that copyright cannot vest in collections of facts, so there is nothing to licence, and reuse cannot be controlled in this way.
CC BY-NC-ND 4 recognises the database right, and speaks of it in s4a:
for the avoidance of doubt, Section 2(a)(1) grants You the right to extract, reuse, reproduce, and Share all or a substantial portion of the contents of the database for NonCommercial purposes only and provided You do not Share Adapted Material
The licence does not define a substantial portion; I would read it as larger than de minimis, which would permit what you propose by way of subset distribution. Unfortunately, CC BY-NC-ND 3 has no similar language.
Regarding the question of informing the execution of a program with the subset of a database, and the subsequent licensing of the program's outputs, the question is very muddy. I can find no guiding precedent on the subject. I am inclined to think that such an arrangement does not create a derivative work, but the chances of me being your judge when the database creator hauls you up in court are very slim indeed.
In summary, I think this is very messy. I see no clear and generally-valid set of permissions that allow your proposal, although you may be able to do it in some jurisdictions. I think you are much better off contacting the database rightsholder, explaining your proposal, and asking them if you may do what you propose. Either they don't really care, in which case they're likely to give you much clearer permissions, which would hopefully extend to distributing a copy of the database subset alongside copies of your program, and under much clearer licensing terms. Or they do really care, in which case you can avoid the unpleasantness of a later lawsuit by allowing them to forbid it now for the price of a stamp.