I hope this app is legit and not a clone or phishing app.

For your issue, because you can't download the app in playstore probably because of country limitation of the app. On this URL https://poloniex.com/app-download you can download the app (apk) directly on their site which is the best way unlike downloading it from external sources.

Now, since they want you to verify your identity, i hope your nationality or current ID or location will not hinder the verification process knowing you can't access the app in play store for country limitation issue or say banned countries.