<p>(1) You pick the desired dimensionality, as a meta-parameter of the model. Rigorous projects with enough time may try different sizes, to see what works best for their qualitative evaluations. </p>

<p>(2) Individual dimensions/elements of each word-vector (floating-point numbers),  in vanilla word2vec are not easily interpretable. It's only the arrangement of words as a whole that has usefulness – placing similar words near each other, and making relative directions (eg "towards 'queen' from 'king'") match human intuitions about categories/continuous-properties. And, because the algorithms use explicit randomization, and optimized multi-threaded operation introduces thread-scheduling randomness to the order-of-training-examples, even the exact same data can result in different (but equally good) vector-coordinates from run-to-run.</p>

<p>(3) Basic word2vec doesn't have an easy fix, but there's a bunch of hints of polysemy in the vectors, and research work to do more to disambiguate contrasting senses. </p>

<p>For example, generally more-polysemous word-tokens wind up with word-vectors that are some combination of their multiple senses, and (often) of a smaller-magnitude than less-polysemous words. </p>

<p>This <a href="https://dl.acm.org/citation.cfm?id=2390645" rel="nofollow noreferrer">early paper</a> used multiple representations per word to help discover polysemy. Similar later papers like <a href="https://arxiv.org/abs/1610.07569v1" rel="nofollow noreferrer">this one</a> use clustering-of-contexts to discover polysemous words then relabel them to give each sense its own vector. </p>

<p><a href="https://arxiv.org/abs/1601.03764v2" rel="nofollow noreferrer">This paper</a> manages an impressive job of detecting alternate senses via postprocessing of normal word2vec vectors. </p>
Using Word2Vec for polysemy solving problems
<p>I have some questions about Word2Vec:</p>

<ol>
<li><p>What determines the dimension of the result model vectors?</p></li>
<li><p>What is elements of this vectors?</p></li>
<li><p>Can I use Word2Vec for polysemy solving problems (state = administrative unit vs state = condition), if I already have texts for every meaning of words?</p></li>
</ol>