Contacting EiC on social media
I personally don't think that neither "ethics" nor "fairness" are at stake here because if I understood your question correctly what you want to do is simply ask a question using an informal method of communication. I don't see how this can create an unfair advantage to you or even raise ethical issues since the question alone doesn't mean things will get done more quickly/unfairly. You simply want a status update on your paper.

However, I also don't see how such course of action can help you. You should also take into consideration that these things to take time and unless you have a pretty urgent reason, it might not be worth asking it again. Sometimes the EiC is having trouble finding a suitable reviewer for your paper or the reviewer itself isn't finding the time to read your paper (keep in mind that they're usually invited to do so, without any remuneration), sometimes older issues of the paper are delayed... my point is: whatever is going on, it isn't good for the EiC either and he's probably already taking the measures necessary.