It is still possible to download all entries via the api and sort them by the timestamp. Removing the cursor data would be one way to mitigate this.
Currently there are a bit more than 43000 entries.
As far as I have seen, only the results are stored. When I entered a random name, only a similar name was found, and that similar name result was stored, but not the original input.
All the data is still public. There are more than 104000 entries now.
The original name, that was searched, is also stored in the data (in another field; somehow I missed that before).
@tourtlesoup: Why don't you restrict the access and why don't you put a warning on your page?