Is it possible to still get some or any STD's after having a full hysterectomy?
I was pretty sure at the time of the op, that I was told I could not get most of them like Chlamidia, but not sure.

If you are exposed, then yes there is still a risk. There is still a risk of a tubal pregnancy if only the uterus was removed and the ovaries and fallopian tubes remain intact also.

I hope it wasn't the doctor who led you to believe that. Even if that were partially true, it shouldn't change the way you approach STD/STI's. That is to say, prevention or testing.

I am lost to answer this one. You can get an STD regardless of your hysterectomy..