I understand applicants are in anxious waiting mode post-interview, and I know it's not fun, but in the spirit of trying to encourage applicants to stop stressing over the part they can't control:
You can't do anything post-interview to increase your chances. Some percentage of the decision is made pre-interview (by choosing who to interview and having a sense in advance of how interviewees rank), most of the decision is fairly instantaneous during the interview, and a small part of it is negotiating the allocation of offers post-interview (the faculty have to meet to decide which of, for example, the 8 outstanding applicants will be offered the 6 available slots). There is nothing you can do to enhance the faculty's opinions of your fit after the interview day itself.
If, and ONLY if, you end up on a waitlist, you can reinforce the faculty's perception of fit by reiterating your interest in that program and your hope for a spot, which still won't increase your chances, but obviously will keep you in the running (whereas other waitlisted applicants might accept offers elsewhere, or indicate in some way that they prefer a different program).
You can do something post-interview to harm your chances, however. My current colleagues and I are not fans of the occasional applicant who sends multiple emails throughout the post-interview period, who calls the administrative staff to ask about their status in the absence of another offer, who emails us or the current graduate students with inappropriate followup questions and/or inappropriate tone, who try to negotiate for a larger stipend, etc. But you wouldn't do any of that anyway, right? 🙂
About the "casual" conversational style of many interviews, well of course. We faculty are not corporate recruiters, we're clinically trained, and many of us prefer a day of interviews that feel like comfortable conversations with smart prospective students rather than Q&As. Remember we're each meeting with a lot of people that day, too! Just be careful to remember that it IS an interview, regardless of how informal it feels.
To the numbers issue: a faculty member who interviews 5-6 people for one position is betting that 2-3 will take offers elsewhere (i.e., they'd be a great fit, but THEY prefer a different program), that 1-2 will tank the interview (either egregiously, or by demonstrating a mismatch between the application materials and the reality), and that 1-2 will be a great fit on both sides.
Short answer: for this phase of the process, your job is done.