When we talk about AC current, is it peak current value or average value?
When we talk about AC current, is it peak current value or average value?

Typically, when someone says that there is, say, 10A of current (AC) flowing through a load, they mean 10A AC RMS.
The average value of a pure sine wave signal is zero.

Also when we measure AC current with a multimeter or a clamp meter, is it peak or average?

Multimeters and clampmeters measure RMS

I mean, if with a multimeter I measure a 1A current under AC110V, is 1A an equivalent value, and does it mean it is 110W like DC?

Yes. That is exactly why we use RMS instead of peak.