Does Arduino run AC or DC
As a general rule, any modern electronic device with computational ability has to use DC. The reason is that they use specific voltage levels to indicate binary/logical states (i.e. 0's and 1's).

In theory, an ideal DC supply (Direct Current) should provide a constant voltage. That allows the circuit to effectively turn it on an off to represent binary states. (In reality, there's no such thing as truly "off" though, because voltage is relative.)

However, the voltage from an AC supply (Alternating Current) is constantly varying. If you plot it on a chart, you should see a nice sine wave, flowing smoothly between positive and negative several times per second. Hypothetically, if a digital circuit tried to use AC then it would get very confused, because everything would seem to be turning on and off all the time.

With all that said, it's very common to turn AC into DC through a process called rectification. For example, that's what allows DC devices to get power from an AC outlet (e.g. to run your computer or charge your phone).