What cable system? Any shows that have copy protection applied will not be able to be transferred.
Any shows on the Premiere recorded in HD will not be able to be transferred to a Series 2.
How is the Tivo supposed to know what your son wants to watch?
Your son will just have to set up transfers manually, in advance for when he wants to watch TV at the spur of a moment.
A series 2 can download content from Amazon, but it's not free. You have to purchase/rent the material.