Elemental opens at level 70.
> Appears under Battle > Remnants of Magic
You get one run per day, automatically resets at server reset (00:00) - you can buy more runs if you wish but it will cost you gold.
As to the runes that go in the Elemental(s) it seems they currently only come from events/shop. To get these you need to open Rune Boxes (the one that looks like a present box - not the one that looks like a chest with a bunch of gems coming out of it)
Elemental processing stones which are used to swap stats are currently set as a level 80 item, which means that if you try to auto use to bring up the menu, it will say that your level is not high enough. Using a processing stone will grant you new randomized stats, unless you locked that stat before using the stone. The max number of stars for the stats are dependent on the quality of the elemental.
If this follows other games, then blue will max at 6 stars, purple max at 8 stars, yellow/orange/red (unknown)
Hope this clears up everything.