Safety of using microcontrollers such as Arduino
The biggest risks are that they destroy the equipment, not that they get hurt.  At least not until you introduce them to soldering irons!

I would recommend not using lithium ion batteries for power - since they can explode if shorted.  Regular AA batteries will get hot if shorted (enough to cause burns/fires after awhile) but arent likely to explode.  The best power supply would be one with an adjustable current limit which helps avoid damaging equipment or people.

Some components like capacitors can explode if run over their voltage rating or with polarity reversed - sometimes with a very scary bang.  But even that isnt too risky unless it gets in your eyes.

As long as they dont do anything incredibly stupid they will be fine.  Electricity at the voltages used in microcontrollers isnt going to hurt anyone.

(As an example of "incredibly stupid" - in our high school electronics lab someone decided to find out what happens if you short out a 120v electrical outlet with a piece of solder.  The answer is that it glows for a second, then violently explodes and sprays molten solder a good 10-15 feet. I recommend not repeating that experiment!)