Why not 'niemand wilt eten'? Do pronouns like niemand, iemand, idereen use the 1st person verb conjugation?
No, it's because willen is irregular:
Mustn't it be like "Niemand wilt eten"?
Willen is irregular. The 3rd person singular conjugation is wil.
Doesn't this also mean, "no one wants to eat"
No it doesn't because food is a noun not a verb. What you could say is: niemand wil te eten.
Would "Niemand wil wat eten" translate as "No one wants any food"?
I would translate 'Niemand wil wat eten' as 'Nobody wants to eat'