Can I download iphone apps from the online iTunes without having access to the iTunes program? I'm not going to have access to my iTunes on my home computer nor my iPhone today. But I would like to download a few apps that are on sale today only (like this one). Is there a way to do that? Or maybe not download them, but earmark them in my account to download later?
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.