No programs I applied to required the GRE, I think that's not a common thing. Some MD-MPH programs did require it, but none of the MD-PhD ones that I saw.
I didn't talk to any PIs before applying. I did some basic research to confirm that a school had research I'd be okay with doing (didn't have to be a perfect fit, but at least ballpark). I made sure there were at least 2 or 3 PIs doing that kind of research there just in case one of them didn't work out. Then applied and waited to see where I got interviews. For interviews most schools have you pick PIs to talk with when you visit so I chose the ones I wanted and met them for the first time at the interview. IMO it doesn't make a lot of sense to get invested in a specific PI before you've got an acceptance in hand at a school because the odds of getting into any one specific school are already super low and you kind of just have to take what you get.
Related to that - if you know what type of research you're interested in doing, I'd highly recommend doing some digging on schools BEFORE you pay money to apply to them. Some schools are completely fine with Public Health PhDs but the only pubh research going on there is related to some obscure thing (smoking cessation, obesity, opioids, etc...). I applied to way too many schools that allowed a pubh PhD without realizing that I was completely uninterested in the TYPE of pubh research that was going on there. Save yourself some money and don't do what I did. 😛
Hopefully a current student can chime in and give you their perspective too. 🙂