> Then they will go away to eternal punishment, but the righteous to eternal life.
Diction mattered a great deal to Christ. Gehanna (Hebrew: Valley of Hinnom; גיא בן הינום) was a location in Christ's time, that was likely associated with burning, destruction and loss - things that one might be expected to feel in the absence of the Creator.
Hades was where all dead went and remained until the day of judgment. Christ's reference to it as Paradise implies it isn't a place of suffering. Catholicism's Limbo implies it is a place of waiting.
The modern notion of Hell as a location dedicated to the eternal suffering of man, is quite different from either of those places.
Did God create this place?
One view[1][2] is that Hell isn't really a place, but rather a state of being, and the primary suffering of Hell is the separation from God[3]. God didn't create it, rather we ourselves created it by separating ourselves from God through sin.
[1] https://www.stbensduluth.org/blog/fr-joel-hastings/who-creat...
[2] https://en.wikipedia.org/wiki/Christian_views_on_Hell#State
[3] https://www.vatican.va/archive/ccc_css/archive/catechism/p12...
Jesus talked about people being in Gehenna (burning trash dump outside Jerusalem), Hades (Limbo or Paradise, Sheol in Hebrew) and I think Tartarus (deep pit). Tartarus may be OT only, I can't recall ATM.
All those terms, each with it's own intent and meaning, were later rolled into Hell (which received a new meaning, one different from any of the original terms). This was eventually codified during one of the Ecumenical councils (1st council of Nicea?)