Is it possible to remotely install an app on an iOS device from the web/iTunes?
Yes - iOS supports this out of the box with many MDM frameworks to push updates to iOS devices over the air. There are some free / open source MDM, but I would recommend something hosted like bushel that has better support and has been running a while. 


http://bushel.com


If you need to host the MDM yourself, Apple's server app includes Profile Manager and would be my recommendation for your first server. (It's well documented, inexpensive, handles sertificates well and enables push notification registration.)


https://www.apple.com/osx/server/