How come the role of the Apis mellifera is determined by nutrition rather than chromosomes?

Prior to making my question I browsed on similiar question such as this one but it doesn’t specifically addressed my doubt in the sense that it is related with a different species and on a concept not mentioned in that question. More specifically on whether does nutrition may influence genetics on the sex determination or not?.

My doubt arises as I’m learning about Partheneogenesis and genetic determination of the sex. Upon reading this entry in Wikipedia, it explains that a queen bee of the Apis mellifera is determined during the development of the larva. The article doesn’t state anything about the chromosomes of the larva. It just states that the queen will develop into that by feeding it from royal jelly, from which I believe it has some sort of protein that may influence the development of such larva giving it their characteristics.

But this topic is letting me confused. Does this means that for example a male bee can become into the queen?.

This article explains that some insects produce haploid males from unfertilized eggs by I believe Partheneogenesis. But if the bee doesn’t mate, how is the sex determined?. I believe that it will produce only females (as his genetic sex determining chromosome is ZW?) and as such will yield only females, but if the queen does successfuly mate with a male may produce males which in turn can also lay eggs (by Partheneogenesis) and those eggs will all be males?.

From this I’m getting the conclusion that it can occur that some individuals may be all females or all males?.

How come is it possible for an haploid organism get into full develpment isn’t it necessary to be diploid?. Do they become into diploid at some moment?.

Can someone help me to clear out this doubt?. This topic has left me confused, so an answer which would help me the most is some sort of explanation on the concepts of partheneogenesis and sex determination in the bees.