Increasing the number of authors in the research article after uploading it on arxiv
I imagine that there is no problem from the side of arXiv: submissions there are versioned, so you can always update a preprint there. arXiv also explicitly allows you to submit the same work to a different venue later on.

The problem with your process is that you do not seem to have a trust relationship with your second author. If your second author does not want your joint paper uploaded to arXiv and (i) you do it anyway, and (ii) do not even make him an author even though he was part of the research, then what does this say about the relationship the two of you already have? And what does it say about the kind of relationship you hope to have with him in the future? If I were that second author, I would consider uploading a joint paper over my objections a major breach of trust. I would not ever want to work with you again.