Does Arxiv count as publication?
No, it's not considered a published paper in the usual sense of peer-reviewed publications. ArXiv is meant as a preprint server where you upload preprint versions (essentially polished draft versions) to quickly disseminate your research, before submitting it to a scholarly journal where the paper undergoes peer review. Only after the paper has been peer-reviewed and published by the journal do you have a "real" publication. (Depending on your agreement with the journal, it's then possible to update the arXiv listing to reflect revisions made to the manuscript during the publication process.)

It's still appropriate to list such preprints on your CV - especially early on in a career, when you might have few peer-reviewed publications. This is fine as long as it's made clear that these are preprints, or manuscripts under review or similar.