When trying to understand how the electromagnetic force works in a Quantum-Mechanic context (what mediates it), one concept you will quickly encounter is that of virtual photons (and more generally virtual particles). However, once you try to research them a bit further than the most basic of explanations, you will find a variety of statements that don't seem to be very consistent with each other.

If you look at this website for instance, questions about the existence of virtual particles have answers that vary from yes to they're mathematical tools to no and in different instances of the question the most upvoted/accepted answer might be different. This is of course confusing as it is not clear which version of the answer is more accurate. I think an attempt at clarifying what's actually the case should be made. The purpose of this question is to ask people not only to give their perspective on it, but to explain it in the context of the other perspectives as well.

Here are a few statements I've often seen in relation to this topic:

1. The photon is the mediator of the electromagnetic force.
2. Virtual particles are exchanged during interactions of particles.
3. Virtual particles are mathematical tools that are useful for making calculations in QFT.
4. Virtual particles are mathematical artefacts of perturbation theory. They don't exist in non-perturbative approaches.
5. QFT describes fields and their excitations. Particles are a regular type excitation of the field. Virtual particles are a non-regular disturbance of the field.
6. There is a physical phenomenon that could be loosely named as a "virtual particle" or "exchange of a virtual particle", although it's not best or most accurately described in terms of particles.
7. Virtual particles don't exist.
8. Virtual particles cannot be observed.
9. Virtual particles exist and they have observable effects (e.g. the Casimir effect).

Some of these statements are contradictory to each other, or it's not immediately clear how they can be true at the same time, yet they're all things that have been claimed as true by different people. The problem is, however, that they don't usually address the contradictory claims, so it's hard to judge their merit since they are not a holistic answer that addresses everything, nor can different answers easily be compared since they address different parts of the topic.

For instance, take statements 1, 2 and 7. It can easily be seen that no more than two of these statements can be true at the same time. If someone holds at virtual particles don't exist, then it's an obvious choice to say that 2. is untrue. However, in that case one has to ask "In what way is the photon the mediator of the electromagnetic force then?". This question is not usually addressed, however, when people dismiss virtual particles so swiftly.

So, essentially what I'm asking is to address whether or not the above statements can be said to be accurate according to our best knowledge of physics and to address them in the context of each other (i.e. why is one true and the other is not; why can two seemingly contradictory statements actually be true at the same time).