Yes you're right that it isn't mentioned anywhere on what happened to Herpo the Foul's basilisk. Given that Salazar Slytherin basilisk had been in Hogwarts for approximately 1000 years since he built the Chamber of Secrets, and Herpo the Foul's basilisk was alive during Ancient Greek times, we have concluded that it would indeed be dead by now. Most likely the basilisk remains would be hidden somewhere in Greece or wherever and maybe in a labyrinth somewhere so it's really hard to find, so feel free to have Amaranth go looking for them. ^^
As for your other question, if the application has a good reason/plot as to why the unnamed person is trying to obtain or make a basilisk with a lot of information, we will be happy to look it over and discuss it. ^^
I hope that answers your question
