Help me understand how word-as-vector representations are constructed
I am assuming that you mean a vector representation of words, not to be confused by the vector representation produced in a bag of words approach that represent a document in vector space. Word2vec is an approach in which you train a model to represent words as a function of the provided context. 

The answers that follow are: 


1) No: You'll need some representation of context in which the word is used. For example: Skip-grams.
2) No: That is a user defined parameter
3) &lt; I do not understand this question >