Is this true: "At over 700 Hz, current simply flows over your body"?
Skin Depth
The human body does have a "skin effect" but it's not as thin as you might think.
Electric currents are confined to the outside of a conducting body, but humans are not very conductive, so the fields penetrate quite deep.
The best example that comes to mind is 2.45 GHz - we all know that a microwave oven cooks about 2 or 3 cm into a piece of meat - this penetration depth is closely related to the skin depth.
The primary reason that you don't feel high frequency current is that the nerves and cells can't respond to anything above ?about? 1 kHz. I've discussed this in a previous answer, more about the safety aspects than the skin effect itself, but it might help.
Nerve effects are the primary cause of injury due to electricity, mainly the heart of course. If the frequency is high enough that it can't influence the nerves, then all you have to worry about is the heating effect. For a potentially lethal 100 V at 20 mA, only 2 W is dissipated in the body, which is insignificant compared to the 200 W of normal body heat (though it will be concentrated at the entry and exit points). So at high frequencies you can carry a much higher current than would be lethal at low frequencies, possibly without pain or injury.
High voltage and lower current
It's not true that the current is lower at high voltage. In fact, a higher voltage will usually cause a larger current to flow, than a low voltage. High voltage overhead transmission lines might be 400 kV but they also carry hundreds of amps.
When it comes to human safety, higher voltage are almost always more dangerous.
This isn't true.
It's perpetuated by a misunderstanding of a real phenomenon called skin effect:
Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor, and decreases with greater depths in the conductor. The electric current flows mainly at the "skin" of the conductor, between the outer surface and a level called the skin depth. The skin effect causes the effective resistance of the conductor to increase at higher frequencies where the skin depth is smaller, thus reducing the effective cross-section of the conductor. The skin effect is due to opposing eddy currents induced by the changing magnetic field resulting from the alternating current. At 60 Hz in copper, the skin depth is about 8.5 mm. At high frequencies the skin depth becomes much smaller. Increased AC resistance due to the skin effect can be mitigated by using specially woven litz wire. Because the interior of a large conductor carries so little of the current, tubular conductors such as pipe can be used to save weight and cost.
That is, for a uniform conductor, an increase in frequency will result in a diminished component of the current flowing through the middle of the conductor - higher concentration towards the circumference, the "skin".
Skin does not transpose to skin, be it human skin or another membrane over another conductor. If a conductor of akin to the skin's epidermis was constructed, higher frequency still wouldn't concentrate to the outer surface.
There is a field within biology called bioelectrical impedance analysis (BIA) which relies on the varying frequency response of cells and other biological matter.
This is not true, in fact it is possible to "cut" flesh with a high frequency electric current.
http://en.wikipedia.org/wiki/Electrosurgery
An alternative name is "RF knife" because (as pointed out by tomnexus) at high frequencies the electric current has no effect on the nerve cells.
One advantage of using this kind of "knife" is a lack of bleeding, because the "knife" burns through the flesh rather than actually cutting it.
From personal experience: I had a small benign tumour removed using this method. They placed a return electrode of large area on my thigh and cut the tumour from the surface of my abdomen with a small pointed tool. There was a faint whiff of burning flesh (and of course no pain during the operation due to the local anasthetic, though there was some afterwards.)