Can people see what I download on my iPhone?

Through iTunes or something else? Just curious…

No. Unless you give them your Apple ID or you let them see the contents of your phone.

Apple knows what you download through iTunes, but they're not supposed to look. Other downloads are more or less private, although obviously spook agencies like the NSA have ways of monitoring network traffic that would allow them to see what you've downloaded in certain cases… If they cared, which they almost certainly don't.