You can short circuit using your body and you'd probably feel a tingle (your body resistance is not high, but not too low either). But if the ring you're wearing on your finger is causing the short circuit, thousands of amps will flow through it, as it has an ultra-low resistance, and heat it up to temperatures that will quickly cause burns and whatnot.
If the device does not have infinite amps, then this is the case where normally the power supply's fuse would blow, and thus the ring would never heat up and nobody would get hurt.
To summarize: Low-voltage, high-current electricity is indirectly dangerous, whereas any high voltage electricity is inherently directly dangerous.
Very high voltage with very low current is not inherently dangerous. Static electricity is this case. The total energy (voltage x current x time) passing through the body is the critical determinant of harm.
No. But you'll be injured if you short it with any metallic objects while touching it, like the wiring, the board, your probe, the ring on your finger, etc.