Do most people want to murder? It seems like the most popular theory among philosophers and neuroscientists who believe in free will is something called free won’t. This basically means that we cannot will what we want to will, but we have the power to veto a thought that our brain has produced.

This would mean that a person who is about to murder another person should have the power to veto pulling the trigger- but if they don’t, then they should be held morally responsible because they didn’t use their free won’t power. 

Now, I don’t think about murdering people, but I might be a weirdo. Do most people want to murder other people, but they use their free won’t to refrain- so that they should be praised for their self-control?
[Just addressing your title question:] supposedly so, but there isn't a lot of data on this. One of David Buss' students has this in his PhD thesis:


  participants from the Austin
  community completed a survey instrument that asked a series of questions about their
  most memorable fantasy of killing someone else. Seventy-six percent of women and 91
  percent of men reported having at least one homicidal thought in their lifetime. The
  person both men and women most frequently thought of killing was an intrasexual rival.
  The majority of homicidal fantasies involved the murder of someone who was not a
  genetic relative. Men were significantly more likely than women to have a murder
  fantasy triggered by a romantic partner’s infidelity. Women were more likely than men
  think of killing a rival who damaged their sexual reputation. These and other findings
  were predicted in advance by Homicide Adaptation Theory [HAT] (Buss &amp; Duntley, under
  review). 


As you can probably tell, their angle is evolutionary psychology; they don't care about any free will debates, it seems. I could easily find a criticism of HAT by Durrant (2009), which cites several works of Duntley and Buss on this; the latest cited in there being:


Duntley, J. D., &amp; Buss, D. M. (2008). The origins of homicide. In J. D. Duntley, &amp; T. K.
Shackelford (Eds.), Evolutionary forensic psychology: Darwinian foundations of crime
and law (pp. 41−64). Oxford: Oxford University Press


A more recent paper Reynolds &amp; McCrea (2017) summarizes a few of the older studies on prevalence:


  Unfortunately, there is a paucity of
  research on homicide fantasies, with most of
  the research historically focused on criminals
  or the pathological [...] This tells us little about the psychology
  process of homicide in typical individuals.
  Kenrick and Sheets (1993) conducted
  two studies with college students as subjects
  to address just this limitation. In the first
  study, participants were asked about their
  most recent homicide fantasy, and in the second
  study participants were asked about their
  homicide fantasies in several contexts.
  Results indicated that the majority of participants
  did have at least one fantasy, with
  males recalling more homicide fantasies
  (e.g., 73% vs. 66% in Study 1), and males
  reporting longer and more detailed fantasies.
  Results were interpreted as supporting evolutionary
  explanations for homicide like the byproduct
  hypothesis.
  
  Crabb (2000) also found that homicide
  thoughts were common in normal
  undergraduates. Crabb investigated homicidal
  thoughts and the weapons used in these fantasies.
  Similar to Crabb, Kenrick and Sheets
  (1993) explicitly asked undergraduates questions
  concerning their thoughts about killing
  someone. Replicating previous research, most
  participants admitted to a homicide fantasy.
  Results also indicated that homicide fantasies
  were preceded by a threatening interpersonal
  event and involved weapons like firearms, knives,
  and clubs, rather than weapons like hands
  and feet. The evidence was interpreted as supporting
  the existence of evolved psychological
  mechanisms able to associate material–cultural
  implements, like firearms, with aggressive
  actions and to rehearse this through fantasy.
  These studies are important as they demonstrate
  that homicide fantasies are common and
  unlikely the result of pathological processes.
  Furthermore, they support evolutionary explanations
  for homicide like the by-product hypothesis
  and homicide adaptation theory.


Reynolds &amp; McCrea's study tried to elicit subjects to spontaneously think of murder by providing them with some typical contexts in which murders occur, but they weren't terribly successful at this: less than 5% of participants reported such cued homicidal thoughts, although many more reported violent thoughts.