Ok Mentalist, but remember you asked! lol
First, I think he confronted her very early on as she was found somewhat close to where the parking lot and her car were. He was probably (maybe) sitting on a bench in wait for anyone and then she pulled up, got her things together (obvious she was going on a run), and then started down the trail. He may have figured she was going to start running and got up and started off before she did. Either way, he subdued her (probably a blow to the head - blunt). That way he could carry her like you normally would carry someone who has passed out - both arms out in front with person cradled. He can carry her that way down a trail so IF detected he can pass it off as she "passed out" or "fainted" or whatever (common for a runner to do).
He carried her to where they found her. You're right about the shoes - probably falling off. Don't know if she ever came to (I, for one. hope she never did) - if she did - she fought - hence possibly the other shoe.
Where she was found was out of sight, hard to see. The entire crime was commited there. We haven't seen another other "site" being roped off and disected, which would lead to believe two scenes (one where he killed her and the other being the burial site). Nope, we've have seen and heard of only one site.
Your post-mortem comment caught me because that has come up in discussions I have with "real life" people - lol. I, personally, don't think so. But, he likes to beat. We saw that in the docs of his first crime - beat that poor lil 13 yr old about the head horribly. He beats and rapes at the same time so its possible that in the commission of the whole event he could have killed his victim and the rape happens post-mortem.
I think he's escalated as far as weapons. I think there is a knife. I think that's why we're not being told COD - kinda obvious if COD is by stabbing or a slit throat. I think the knife they have has other, "older" DNA on it (maybe Amber's).
This one subhuman hunk of flesh is real, real bad. He "blacks" out during his crimes and does horrendous, horriffic things.
How many victims he really has - we will probably never know.
And that's what I think (and it really hurts to think it).