iCloud is the proper name for the Apple Product and is unrelated to your Verizon Wireless account. But sometimes account reps at Verizon will refer to the Verizon Cloud as "Verizon iCloud", so there may be some confusion there.
No - the Verizon Cloud is a Per Line feature normally billed per line, and having separate storage repositories. Getting VZ Cloud for one line will not make it appear on any other.
Yes - with the recently introduced "2TB Shareable Cloud" you, as account owner, can add Verizon Cloud to any of the lines on your account and you all draw from the same 2TB total storage amount but all content is still private per line. In this case there is one charge to teh Bill for however many lines you have, so it's a deal if you are looking to have more than 3 lines with the VZ Cloud storage on it.