Time paradox always occurs whenever there is time travel, its not just limited to TWGOK. The main question is, if they alter the past, then the present should not exist.
TWGOK solves this by switching the 2 Keimas' consciousness in each timeline, and then having the future Keima lay the groundwork in the past. By leashing up all the girls who would be bonded to the goddesses, he allows all the goddesses to be within reach (aka be in the same school) when he needs to awaken all of them in the future.
This is why all the goddesses were conveniently in the same school. Its not a coincidence, but its also not because the school was special. The situation was literally engineered that way by future Keima. It was also why he would succeed, because he had already done it.
In the event he would fail or make a wrong decision, he left notes for Tenri, which is also kind of the reason why she moved back to the neighbourhood around the time when the goddesses were needed. Everything explains itself.
Elsie though, I'm still completely confused about her.