To remote play/stream iTunes content from your computer to your iDevice, you need to activate Home Sharing on both iTunes on your computer AND on your iDevice under the Music and Videos settings panels in your iDevice's Settings app.
Some iPhone and iPad apps of the same app and version are different and take advantage of the iPad's lsrger screen and require that you pay for both an iPhone and iPad versions.
This stated, in the iOS App Store, if you tap on iPhone only, you CAN find and download the iPhone versions you purchased for your iPhone and download them to your iPad, but you will need to tap the zoom button at the bottom corner of the iPhone app screen to enlarge it to fit the iPad's screen or leave it at iPhone size screen.
Good Luck!