I'm about to try to do the worlds first 100% for the mobile version and I'm wondering if I'm allowed to use an emulator such as this

https://www.bluestacks.com/apps/strategy/plants-vs-zombies-free-on-pc.html

If not could I use a different emulator instead because being able to do it on PC would be a huge help

Yes, emulators such as Bluestacks are allowed. There are runs on the leaderboard such as ymblcza's old WR and my Any% run from 2019 that are played on Bluestacks.