locate lost phone with help from gps and web based google play Phone lost but access to google play through web interface.
Is there any app that will send GPS position right upon installation,
or send the phone position to the gmail account installed on the phone (also remotely available of course). 

There's the app "Plan B" but only for android 2.0-2.3.

Regards,
If you have enabled Android Device Manager as administrator

You can either use the mobile app on another phone to track it or use this link:
https://www.google.com/android/devicemanager