Can I just leave this outside? Does it withstand severe climate like rain and heat?

Yes, you can, it is an outdoor screen but it requires some care in order to remain usable for a long time. We suggest keeping it covered when not in use, avoiding direct sunlight exposure (it is a plastic, after all)
Of course, if you want to enjoy a late night movie or you want to play video outside, you need a stand to hang it on and it will perform flawlessly.

We don’t recommend exposure to heat and sun. While rain has no direct impact, if the environment is muddy it can get dirty and require cleaning. Normal operating conditions (at night, in mild weather) should cause no harm to it.

For more information please check out our guide setting up a great backyard setup
http://outdoormoviehq.com/ultimate-guide-to-outdoor-movies
Or take a look at our recommended projectors and screens
http://outdoormoviehq.com/outdoor-movie-screens