how to train custom word2vec embeddings to find related articles?
I find your question bit convoluted, so I will answer with the following bullet points:

Train your own word embeddings: There are many implementations out there, gensim is one.
Find related articles: On that point, without being an expert, I would suggest to do some research on Topic Modelling. There are also a lot of libraries you can use.
Word embeddings to sentence embeddings: This process is not as straightforward, the semantics change just by adding words together. You can use Word Mover's Distance or numerous other which train in a supervised way sentence embeddings or unsupervised.