Queries regarding the working of "Word2Vec" vectorizer to convert text to numeric representation

I worked on a predictive (classification) model. I used Word2Vec to convert the data is textual columns to numeric, following which I ran the machine learning algorithms.

I have the following doubts regarding the working of Word2Vec:

1. When I check the vector representation of each word of a sentence, I get an array of 100 numbers/vectors. What do all these numbers mean? I know that each number corresponds to a dimension, but what is a dimension in this context (with regard to the vector space)?

2. When training the Word2Vec model on a 'Neural Network', each word in a sentence is fed as input to the input layer & the words are one-hot encoded. So the vector representation of the words being fed would be something like, [1 0 0 0 0 0 0] & [0 0 1 0 0 0 0].

These vectors are initialized with random weights. The weighted sum of inputs is transmitted to the next layer (Hidden Layer). My doubt is, what is the point of assigning random weights to these word vectors when the weights that are being multiplied with the 0s will anyways remain 0?

How is the neural network transmitting information across with sparse data?

Note: I referred to many sources & these questions are being asked based on my understanding. Do let me know if I have interpreted any concept wrong. Thank you.

Regarding the dimension of the word2vec embeddings, I don't know if you can say anything about what a dimension represent. These are vectors in the embedding space, and I would assume that each dimension can correspond to some semantic concept (or a combination of semantic concepts), but it is very hard or impossible to say what each dimension represents. Maybe one dimension may indicate if the word is verb, other if the word is a noun, etc., but these are just speculations.

Regarding the second question, for each word the weights that are multiplied by 0 will be slightly different, as for each word, the position of 1 will change in the one-hot encoding. Thus, at some point in time every weight will have been multiplied by 1. If you have a big training dataset that contains your whole vocabulary, this will happen during training. Otherwise it may happen during testing. Moreover, each neuron has a bias term. So even if the input is sparse, the first hidden layer will not be sparse anymore. Thus, you could interpret the first layer (the hidden layer in your question) as a mapping from the one-hot encoding space to a dense embedding space, where the sparsity is removed.