I think the important question here is not what the average applicant looks like, but what the average
accepted applicant looks like.
Just from reading SDN and talking to profs and current students, many students apply to PhD programs in psychology and simply aren't qualified. Sure, once in a while someone with subpar (compared to others) qualifications gets an interview or an acceptance, but it's likely not representative of how this process works.
Do all the applicants already have a 3.5 or better?
It probably ranges from 2.0 to 4.0, but my best guess is that vast majority of those who actually get interviews and subsequent offers, have a GPA above 3.3.
Do ALL the applicants have research experience?
No, but you likely won't get an interview without any at a reputable PhD program.
I am much better than my peers, but I worry that I am not better than the average applicant, because everyone applying knows how hard it is.
I'm sure it wasn't intended to sound the way it does, but just being a good student in undergrad doesn't cut it for the majority of applicants.
Your questions are a little vague. I'm not sure if anybody knows exactly what the average applicant looks like. What I do know that often time departments toss up to 50% of applications (not always) if applicants don't meet minimum requirements. These requirements are often not set in stone but I think it's pretty safe to say that with a GPA < 3.0, GRE < 1000, and no research experience nobody will seriously consider you at a decent program. Clearly, there are exceptions and I don't know for sure how each program handles it, but given that I've heard multiple people toss around ~50% , my best guess is that a lot of these applicants don't even meet these minimum requirements.