yes,but you can't save data from games.
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In short: no. The Xbox 360 has to install an original Xbox emulator program to run the Xbox games. It stores this emulation software on the hard drive.
If you're going to run your games from the DVD drive then horizontal. If you you're going to load your game onto the hard drive and play it then it doesn't matter.
When the Xbox says install game it does not mean you are about to install the full game onto your hard drive. When you install a game on to your Xbox it's taking some of the game files and installing them to make the game run smoother and possibly look better.
New casing, a new chipset which helps it run cooler and redesigned motherboard and a revised DVD drive
The Xbox 360 and the Xbox One