Using the Monitor RGB profile to display an image on a monitor calibrated to use the same profile is equivalent to turning off calibration, are you sure this is what you want?

You can turn off Proof Colors in the View menu while editing . It's not necessary to keep turned on unless you are proofing an image for a specific viewing environment/print setup, which can be done after all major editing has been finished.

In order for your image to look the same in Camera Raw and Photoshop you need to make sure that they are set to use the same color space. In Camera Raw you set the color space by clicking on the underlined information at the bottom of the interface. In Photoshop you use the Edit > Color settings screen.

UPDATE: The 'Proof Color' option in Photoshop is intended for simulating the appearance of an image on a specific output device, which should be done after general editing is complete. The result of general editing should be an image that looks correct in the working space, which will reduce the level of tweaking required to get the best possible output for any specific device. You can see this question for more details on color management and this question for how to make it easy to get back into camera raw after opening an image.