"When you click Rent, your movie downloads." Downloads to where??? icloud or ??

It depends on your iTunes setting, what device you use and which option you select (rent/buy)...

if you rent a title on the ATV, it will stream directly from iTunes - nothing is stored. (Kinda like Netflix)

if you have the iTunes setting to download any purchases then when you buy on any iDevice (iPhone, iPad, Mac/PC, ATV) then it will download into your iTunes library.

if you rent a title on you iPhone/iPad then the title will download to the device only and you have 30 days to watch it.

you should always download purchases since Apples "rights" to the availability of titles is at the discretion of the studio who owns the title - they could sign an exclusive deal with networks or other providers. If you have downloaded the title then your safe. However, if you don't then you could lose access to it. For example, when Disney pulled titles from all streaming providers...