Time Capsule Questions
Yes, you can connect to it through wifi/cable without the Time Capsule connected to the internet.
Yes, you can just store anything on it.
No, unfortunately not.
I am not familiar with this service. However, you can mount the Time Capsule as an external hard drive and thereby use it as any other backup device.
Like answer 4: if the iOS program allows you to copy files to an external source (FTP/ssh/etc.) you can connect the Time Capsule to computer in your network and access the time capsule drive through remotely accessing that computer. I don't believe that the Time Capsule drive can be directly approached by iOS.