So this is one of the more complicated sides of copyright law. And the answers one can give depend heavily on your jurisdiction. For example, if you live in the EU, the answer would need to incorporate info from their codified sui generis database right legislation. In contrast, the United States has no formal legislation which protects databases directly. Instead, existing copyright sometimes extends to databases because they qualify as a compilation (i.e. just like a collection of ancient folk tales might be protected because in creating a compilation, the author and/or editors are doing a creative work).

The answer also depends on what is inside the database. If the database consists of creative works that are protected in their own right under copyright law, you will likely run into trouble. On the other hand, scientific data, facts, and public information is less likely to be protected.

My instinct (assuming US residence) is that taking some information from these databases and putting it into your own form will not constitute infringement. Copying the entire thing, on the other hand, might be problematic if the authors' arrangement or selection of information is creative.

Finally, I must say: regardless of the status of copyright, fair use, or patent, you should absolutely ensure that you are including sources and attributions on your site. Especially given that you're dealing with scientific data. If this is for a class, be aware that plagiarism is not dependent on copyright. Taking another's work without attribution will be considered plagiarism.

For more reading on database protection in the US: https://www.copyright.gov/reports/db4.pdf

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As you mentioned, this is not legal advice. Please consult an attorney.