Can iron and copper be mixed?

If sufficiently heated, any two metals can be alloyed together. There may not be any special USE for the resultant alloy, but you can do it. There are probably no historical examples of iron-copper alloys because someone did it, back in the early days of the Metal Age, and discovered there was no benefit to it - it wasn't harder or stronger, it didn't hold an edge better - so it never became commonplace.