What is relation between power deposition and frequency?
As we'd expect, the higher the frequency, the greater number of cycles a wave undergoes, and therefore, we would get higher Specific Absorption Rates (SAR). The skin depth at which most of the energy is absorbed will drop for higher frequency waves.
This is true until you hit the GHz where atomic phenomena begin to become relevant. At high frequency, the charge and spin domains from the electro and magnetic components physically cannot change their distributions or directions fast enough and end up becoming saturated and the absorption will go down. Different materials have different frequency responses depending on their exact chemical structure and charge distributions.

Low power EM in the microwave and millimeter ranges are only able to heat up your tissues and it's the same as having an electric blanket on.
So, yes, it's very dangerous to wrap a 1kW electric blanket around your skull, just like it's dangerous to wrap 10,000 cellphones with 100mW WiFi antennas in them around your skull.
If you're worried that the cm-wavelength waves can form standing waves in your skull and alter your thoughts, they can't since all the energy would be dissipated by all the conductive electric jelly between our ears. Also, even if focused, the diameter of the beam will be limited by the wavelength and if you hit higher frequencies, you'll end up with shallower skin depth. If you want to pulse it to get a huge instantaneous energy, you'll run into that problem again. A pulse is the equivalent of the sum of many higher frequencies through Fourier theory, so now you'll have a bunch of high frequency shallow absorbing energy, and you'll be unable to zap people's brains. Those reports of spies being shot with microwave guns are mostly bogus. It's much easier to spike a meal with poison than to use a high powered microwave beam since they, and everyone a block around them would be able to feel and hear it because of the intense power requirements.