What should I be doing to prep (applying next year)?

[CSmeow]

Hi everyone.

I'm considering applying to PhD programs (specifically in Education with a STEM focus) next year. I have a Masters in CS so already have GRE scores and I have professors that would be more than happy to write me letters of recommendation.

I do not, however, have any published research. This would be the weakest point of my application. My grades and references are/would be excellent, and I have an idea of what I want to research. I do not, however, have an exact thesis in mind. I more or less have a "theme" and I was somewhat hoping that my exact research topic could develop after I started a PhD program. Is this realistic or do I need a more specific idea before I apply?

Also, I would like to make contacts with professors in prospective schools to discuss my research interests and perhaps meet them face to face. Would most professors be willing to do this? How would I go about contacting them? Would a simple email be fine? I have points of contacts that can probably introduce me to some, but definitely not all of the professors I'd be interested in working with.

tl;dr:
1) Do I need to know exactly, down to details, what is want to research in a PhD program when applying, or is a general theme okay?
2) What's the best way to reach out to and make contact with professors I'd be interested in working with?

Thanks in advance.