Is it possible to change someone's belief with argument and evidence?

Yes. Obviously.

Of course depending on the "someone" and "the belief", such a change might be easy or hard, but the simple answer to your question is yes.

Yes, but how common is this? It depends on the strength of the person's belief and the strength of the argument/evidence. There are certainly some people for whom their beliefs are part of their core identity, which means those beliefs are virtually impervious to arguments and evidence (virtually). I suggest complementing your rational/evidence-based argument with an emotional argument. You will have better success.

Possible, but like Bo responded, not all that common. One's belief system most often has a high emotional attachment, and desire for a 'sense of belonging,' which is the most important social and cultural motivation of 'belief, which most often overrides the evidence and sound arguments that would motivate one to change one's belief. Of course some do change their belief based on what they consider evidence and sound arguments, as reasons for change, but it is often the case these decisions are not unbiased, and reflect anecdotal considerations.

I say yes. However the change is seldom immediate, thus giving the appearance of "not happening ". We can't Un hear or Un see anything. Once experienced it's in there! As we grow/age/experience we often come across situations that will stir the stored words or sights, connecting dots to the point, so to speak, that one had tried to make, that was missed.

I still believe boiling water is hot and one shouldn't reach into it to retrieve a hot potato. Although there is an instance where a newly found feral child did exactly that and he didn't feel pain and his skin wasn't effected or injured. Kind of an opposite example of what people may claim as being scientifically provenz except for this child apparently.

A few things come to mind, I forget the exact quote and who originated it but essentially you can't win an argument with an ignorant person so don't bother trying.

Another is the backfire effect, which says that as your beliefs are challenged with contradictory evidence, you don't change your mind but your convictions become even stronger.

In my experience it all depends on how firm the belief is, how much face the person your'e attempting to persuade stands to lose, and their level of intelligence.

A Quote by Kenneth Smith on philosophy, thinking, consciousness, intellect, modernity, and truth
in consciousness...

In characterizing realities no less than in taking positions on issues, consciousness generalizes, i.e. genericizes: in articulating or formulating, it reduces things, even our own selves, to forms, abstractions, idealizations, types, archetypes, simplisms. “Thinking” is an activity that ultimately grounds or resolves itself in the satisfying, self-certain form of orthodoxies, preconceptions, uncriticized and imperative norms; and it is overwhelmingly inept to recognize just how pathetic, parasitic or placental is its relation to its “own” fundamental norms of understanding and valuation. Rarely if ever does any act of thinking grow so laserlike or iconoclastically intensive as to escape from the dense miasma of what is acceptable. To think what actually is is even more contranatural for humans than to see what actually is: as subjectivizing as “seeing” is, “thinking” is many degrees or magnitudes more saturated with conditioned biases, delusions, self-deceptions. A program of hygiene or asepsis for the sanity, acuity and clarity of syncretic or wholesided thinking—a discipline of orthotics for sobering, grounding and polemicizing of well-formed gnoseonoesis—is needless to say unknown in modernity. Not just language but virtually all of intellect, education, culture, etc. have been adapted into utilities, tools whose very aspectivity militates against the nakedness of “evidence,” which is to say, against candor and against truth: regardless of what it may be called, “evidence,” even the most obvious and blatant, is in actuality not so “evident” to most people, and the modern development of “sophistication” or “education” typically worsens the obscurantism.