When Hom travels back 3 months to try to save Madoka, does she find a past Homura there or her future "mind" incarnates on her past body? If she finds a past Homura there does she have to kill her past self in order to prevent Madoka and the rest to meet two different Homuras?
Gen Urobuchi didn't think of the mechanics of it too much however we can infer from what he said and what we see is that Homura is reversing time as opposed to traveling back
The weapon that looks like Homura's shield is actually a sand timer. When the flow of the sand is blocked, time is stopped. And when there is no sand on the upper part of the sand timer and then the timer is reverted, one month's worth of time is turned back. But before that stage is reached, only time stopping is possible. This means the special power of Homura is the ability to manipulate one month's time's worth of sand in the sand timer. As for the time passed and then turned back, since it was not the focus in this work, I did not think it through very thoroughly.
when she reverses time we see she wakes up in the same hospital bed where she woke up in Episode 10 before she became a Magical Girl looking like Moemura again as if she hit rewind on the entire universe, but she retains her powers and memories as we see after making her wish she wake up and find the Sand Timer on her arm
Possibly due to her karmic fate compiling, Madoka starts retaining some memories as well as at start of the series she "dreams" of the previous timeline before waking up