Conflict with conference Program Committee
First of all, I don't think there is a "conflict" as long as you don't make this one - and you really shouldn't, as there really is no indication of unethical behavior on their side.

Let's go over your questions.


  Is it normal PC members to ask you change the review score when the review does not vary significantly from the others? I never heard such a thing, even in personal cases where was a large deviation between reviewers.


In many conferences, there is a PC or reviewer discussion phase wherein, after everybody has formed her or his independent impression, these impressions are compared and discussed in one way or another. Optimally, there is physical PC meeting where borderline papers are discussed, but often a mail or forum discussion will do. "Amount of deviation" is not really the right metric to decide whether a reviewer discussion will make sense, but rather whether the paper is borderline or not. There is no point in discussing whether a "Weak Accept" should be a "Strong Accept" if everybody else voted for "Strong Accept", given that the paper will likely be accepted anyway. Similarly, there is little incentive to discuss a "Weak Accept" if everybody else voted "Reject" - the paper is likely dead. For a good conference, "Borderline", "Weak Accept", and "Accept" may just put the paper on the brink where it's not entirely clear on which side it will fall.


  Since my review was virtually the same to the one of the 3rd reviewer, wouldn't it be more fair if all other parties were involved in that exchange? Maybe the 3rd reviewer would have change the score to "0" after reading my response. Why this process should involve only me?


This is a good question, and in fact I think that the model of chairs communicating 1-on-1 with the reviewers is fairly ineffective (as compared to a reviewer forum, for example), although I know a few conferences that handle things like that. That being said, it makes sense to contact the person with the "lowest" rating first. Also, you don't know whether they have also contacted the other reviewers to take your review into account.


  I responded by noting the above and by standing by my initial decision and score because I really felt it did not deserve anything more than "0".
  Do you think my response was appropriate, given the circumstances? Was there any other way that I could have handled the issue?


Sure, your answer was completely ok. Note that, as said initially, you don't have a "conflict" now with the chairs - they asked whether you think your review was too negative given the additional information of the other reviews, and you said no. That's a completely valid discussion to have, and no side acted in bad faith here. From my point of view, there is no "issue to handle", just a conversation that you will have many times over as part of the peer review process.

The only thing that might be inappropriate (depending on phrasing) was noting that it was unfair that they contacted you rather than the 3rd reviewer. As said, this is probably a mail that they also sent in similar form to 2 dozen other reviewers, and they may not quite understand what the problem is. It's not like being asked whether you want to change your rating is a personal insult.


  I think it's responsibility of the PC to have valid arguments for acceptance. Is it ethical to put mild pressure on the reviewer to do their (the PC's) job of accepting/rejecting manuscripts? My job was to provide an honest opinion, which I did. My job is not to push a paper for acceptance because the PC run out of valid arguments.


I think you are overthinking this. I don't ready any pressure at all from the mailing you copied, and I have received similar mails many times over. Sometimes I changed my mind, sometimes I didn't. You provided an honest opinion, and they gave you some more info and asked whether your opinion still stands. I really don't see much agenda behind this.