AppleTV 2 and 3 do not have hard drives only temporary solid state memory.
Even though a movie will prebuffer/download they will free the memory for other functions without warning if you say use the unit to watch a trailer or stream YouTube or from the computer.
They manage slow connections badly - I feel they should retain the downloaded movie in that temporary memory until you watch or allow it to be freed up - the assumption is you have a fast unlimited connection and will not be inconvenienced by a redownload (which would be near instant if you had the 8 Mbps speed recommended for 1080p or 6 Mbps for 720p. 2.5 Mbps for SD).
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Yes - presumably you've set up Home Sharing and can stream from the Mac using the Computers icon to access your itunes library on AppleTV?
If you rent in iTunes you have to wait for the whole movie to download (appleTV lets you watch when it thinks the length of the movie is long enough to complete the download as you watch).
Once downloaded via iTunes it'll stay on the Mac for up to 30 days, but will also be available on AppleTV under a new Rentals column in the Computers section for your iTunes library - Rentals appears along with Movies, TV Shows etc but only when there's a fully downloaded rental to stream from the computer.
One thing to be aware of is that some titles are only available in HD on AppleTV not via iTunes.
You might want to experiment SD vs HD anyway as SD downloads far quicker.