Can I cite a paper published after the initial submission of my paper? I wonder if it is allowed to cite a recent paper, published after the initial submission of my paper. In the revision phase I am adding some missing references and I would also like to refer to some very recent papers. Could this be a problem?
There is nothing special about the initial date of submission.  As such, it is entirely acceptable to add new citations, including for recently published papers, at any stage except for some journals' final proofing (where they really just want to confirm their formatting and copy-editing).  

Moreover, in many cases it is not just acceptable but required, especially given that review may be a very lengthy process.  For example, I am in the middle of a revision right now of a paper that had an unusually long initial review for my field---from first submission to submission of the revision will be nearly 18 months.  In the revision, we will most certainly be citing new work, including some of our own other recently published work, as a necessary part of addressing the comments of the reviewers.

So, in short: yes, cite whatever is useful to cite, regardless of its publication date.