The simplest proof that Peano arithmetic is consistent goes like this: Peano arithmetic has a model (namely the standard natural numbers) and is therefore consistent. This proof is easy to formalize in ZFC, so it's certainly a proof by the ordinary standards of everyday mathematics.

Is Peano arithmetic complete?

The theory of first order Peano arithmetic seems to be consistent. ... Thus by the first incompleteness theorem, Peano Arithmetic is not complete. The theorem gives an explicit example of a statement of arithmetic that is neither provable nor disprovable in Peano's arithmetic.

Are the peano axioms consistent?

The vast majority of contemporary mathematicians believe that Peano's axioms are consistent, relying either on intuition or the acceptance of a consistency proof such as Gentzen's proof.