Max certainly does have Layers. If the Layer Toolbar is not visible, rt-click an empty bit of the toolbar and select it.
Yes, you can freeze objects, either individually or by layer (if the objects are set to "by layer"). You can have them display in Grey, or with their material.
F1 is your friend - this is all in the Help.
Max 2016 (SP1/EXT1)
Win7Pro x64 (SP1). i5-3570K @ 4.4GHz, 8Gb Ram, DX11.
nVidia GTX760 (2GB) (Driver 430.86).