Why can't I download apps on my iPhone 6s
Sounds like this may be an issue with your AppleID. You do have an AppleID already? If not create one, you don't have to use an iCloud.com email address you can use whatever you currently use as your AppleID.

I would log into iCloud.com and check your account settings, security and most importantly, the security questions. Maybe even change your password. Once that is done, sign out of iCloud on your iPhone and sign back in with your new credentials. 

Once you have signed in again, try downloading an app. It will likely ask you for a password but should not prompt for anything else.