Can we say that iron on heating is a fluid?

The answers you have received contain part of the story but are partially missing the main points beyond your questions: i) your starting point and ii) a correct intuitive picture of the liquid-solid transition based on an understanding of the phenomenon accordingly to contemporary physics.

The starting point

It contains a few misleading statements that could hamper a correct understanding of what a solid or a liquid is. When a solid melts, there is no real breaking of forces or bonds. The idea of bonds that are broken is a useless and dangerous idea borrowed from the different case of dissociation of molecules. In the case of a molecule, after dissociation, the fragments move away and we can safely speak about a bond that disappears. In a macroscopic piece of a solid, the melting transition does not change the interatomic distances too much. In some cases (for instance, water or silicon), the liquid phases' average distances are even smaller than in the solid. Moreover, a precise definition of a bond in condensed matter is not easy. However, some progress has been made in the last decades via a topological analysis of the electronic charge density. But the key point is that today there is no unambiguous and quantitative physical definition of bond that can shed light on the microscopic process of melting (and symmetrically, freezing).

In the previous paragraph, I have already mentioned that it is false that there is always less space between atoms in the solid. Often this is the case, but not always. No atom or molecule is appearing or disappearing in any case, whatever is the change of density at the solid-liquid transition. Different densities indeed give a different number of atoms inside a fixed volume, but this happens because due to the average expansion or contraction, a certain number of atoms crosses the fixed volume boundary. No one of them disappears or is burnt.

A correct microscopic picture of the melting transition

The different behavior of many observables characterizes crystalline solids and liquids. However, we should not forget that amorphous solids exist, blurring many possible characterizations of the transition based on the concept of spatial order or, on average static quantities. Dynamical properties remain a much clearer indication of the passage from a solid to a liquid phase. In particular, the apparently simple concept that liquid flow and solid don't is a good starting concept to build intuition on the melting process.

Here, I'll try to underline a few (correct) ideas one can connect to the fact that liquids flow.

1. Flowing implies a large relative displacement of far molecules; therefore, we have to expect a faster decaying with the distance of the correlation functions of a liquid.
2. Flowing also implies a large molecular movement even at smaller scales. Even in a hot solid, non-zero molecular diffusion is in place. However, in a solid, it is better described as a series of jumps well separated by time intervals where the motion is mainly vibrational. Approaching the transition, this process becomes more continuous. The old-fashioned chemical idea of bond-breaking is substituted by an increased easiness for a local molecular motion continuously reshuffling the relative positions.
3. Notice that the previous point allows for understanding the solid-liquid transition in systems interacting via purely repulsive forces as a consequence of varying the pressure, like colloidal systems made by PMMA spheres. Purely repulsive interactions do not allow the introduction of a concept of bond. Instead, the local movement's dependence on the availability of available paths for a local diffusion can be used to provide a unified picture of the behaviors on melting.