Does iCloud require any telephone land line infrastructure to send messages? If all phone lines are down (meaning a local or national phone line outage) and with all cell phone towers being down, is there a way that I could send a iMessage (or an SMS) to other iPhone users by using iCloud Service (your offsite server farm)? 

I am trying to figure out if a Cloud-Push Manager could push my message to all receivers, who are registered.

Is Apple's iMessage proprietary text messaging platform a transmission system that allows iMessages to go directly via satellite to those iPhone subscribes? Even if all telephone land lines are down?
iCloud depends on the internet for transmission of data. iPhones, unfortunately, aren't capable of being sat-phones at this point (by themselves). As long as both the sender and the recipient have internet access, and as long as both are using iMessage (not SMS), then the iMessage should successfully be sent and received. 

There are obviously multiple ways to get internet through which your phone could be connected. As you are aware, one such way is through cellular towers (if functioning), or another option is through a wifi connection (but again, this must have a landline connection as well). It is possible to get internet through a satellite dish and then broadcast that connection via wifi to your phone.

Again, both the sender and recipient must have internet in order to be able to communicate with iMessage.