Yes, the hot wallet receiving addresses would have to be generated before you could create and print the print signed transactions. Otherwise, you wouldn't be able to tell the pre-signed transactions where to send the bitcoins.
I'm not sure what you are trying to ask here.
I assumed that you would have multiple addresses in your paper wallet. Each address would hold exactly 1 BTC. Then each address would have its own pre-signed transaction transferring that 1 BTC from that paper wallet address to a hot wallet address.
Were you planning on something else?
Note: there are some people on this forum who will feel that "safely in the bank" is an oxymoron. They will tell you that you can't trust the bank or the government not to empty out your storage without your permission. For example:
http://abcnews.go.com/GMA/story?id=4832471