Can I publicly mention my paper once it is accepted? Since the paper first got submitted anonymized but is accepted now, can I add it to my publications or do I have to wait until the conference?
In general, this may depend on cultural expectations in your research community and the legal requirements imposed by the publisher.  But for computer science conference papers published by ACM: As soon as your paper is accepted, you an add it to your list of publications, and you can post a copy of the paper online.

Once a paper is accepted, its acceptance is a fact that you can include in your CV and/or your online list of publications.  I have never heard of a computer science conference or journal publisher imposing a press embargo on the existence of a future publication.

ACM's copyright policy explicitly acknowledge authors' rights to post their papers online, even before the paper is accepted, including the following:


  
  Post the Accepted Version of the Work on (1) the Author's home page, (2) the Owner's institutional repository, (3) any repository legally mandated by an agency funding the research on which the Work is based, and (4) any non-commercial repository or aggregation that does not duplicate ACM tables of contents, i.e., whose patterns of links do not substantially duplicate an ACM-copyrighted volume or issue. Non-commercial repositories are here understood as repositories owned by non-profit organizations that do not charge a fee for accessing deposited articles and that do not sell advertising or otherwise profit from serving articles.
  Prior to commencement of the ACM peer review process, post the version of the Work as submitted to ACM ("Submitted Version") to non-peer reviewed servers;
  


In particular, non-commercial repositories in point (4) include arXiv.  (ACM asks for copyright transfer only after papers are accepted, so I'm not convinced that the second bullet is anything other than an acknowledgement that ACM can't control what they don't own.)  However, note that the Accepted Version is different from the Version of Record, or as human beings call it, the camera-ready version—the one that ACM actually publishes.

From a practical standpoint, however, very few computer scientists actually care what ACM or any other publisher thinks.  A significant majority of computer science research papers are available online, either on the author's web page, in some institutional repository, or on arXiv.  You are not only legally allowed to post your work, you are culturally expected to do so.  Although ACM and other CS publishers claim the legal right to go after authors for posting camera-ready papers without permission, they have shown no interest in actually doing so, and there would be a huge community backlash if they did.