Almost every instance of vestigial parts I see I just have to laugh. The hindlegs of a whale? LOL Just because 'science' doesn't know what the purpose is doesn't automatically classify it under vestigial.
Since this is the only point you've chosen to address, I will briefly respond.
Here is the vestigial organ
link you are referring to.
There are 149 articles referenced that support the evidence offered for vestigial organs.
Since you ...
doubt whatever research has gone into this subject
... let's examine just
one of the referenced articles.
Nievelstein, R. A., Hartwig, N. G., Vermeij-Keers, C., and Valk, J. (1993) "Embryonic development of the mammalian caudal neural tube." Teratology 48: 21-31.
In order to read this publication, you will need to have access to pubmed or a university library. Are you able to access scholarly research online?
If not, I can pick another article, one that is available online without a subscription, and we can discuss that.