Can I download iphone apps from the online iTunes without having access to the iTunes program?
You can't buy without iTunes or an iOS device.

You can borrow someone else's device (iOS or computer) and sign in with your account to do the buying and then cancel the download / delete the app.

You could also gift them to yourself, but that is a bit more work and doesn't save you from getting to the point where you would just buy the apps.

As a last resort, you could call a friend and have them gift it to you and pay them later.