Let me first preface this to say that I am using KDE 4.12.2 on Mint 13, so your available options may differ (I also had a computer with KDE 4.8.5 on Mint 13 that I checked).
For the tiling, go to System Settings, Workspace Behavior, Screen Edges. Under Window Management, there is a setting "Quarter tiling triggered in the outer |X%| of the screen. The X value starts at 25% and can't be zero, but can go as low as 1%, so dragging a window only the very top of bottom will quarter tile, otherwise it will half tile. Note that KDE 4.8.5 does not have this option; I don't know in which version they added this option. (Thanks, for making me look into this as the quarter tile thing is silly, but I do like half tiling like Windows 7 has - but at least at 1%, quarter tiling is still available if needed.)
As for shortcuts for these, go to to System Settings, Shortcuts and Gestures, Global Keyboard Shortcuts. Select the KDE component of KWin. The options you are looking for are Quick Tile Window to the Left/Right. They are by default not assigned. Click on them, select Custom, then enter the key you want to assign (it will tell you if the key is already assigned to another shortcut giving you the option to reassign it). There doesn't appear to be a shortcut to return the window back to its original position and size like on Windows 7 (though dragging the window with the mouse does return it to its original size).
Mint 13 KDE: AMD FX-6300, 16GB RAM, GTX 660Ti (2GB), Gigabyte 990FXA-UD5
(with Windows XP and Windows 8.1 VMs on VmWare Player)