She normally has an option about “I’ve misplaced my key” which gives a key, but I’m pretty sure it only exists for players who have run keys before on their account. We’ve all just been doing them for so long that we forget.
Yes, the other methods of obtaining a key are to either run a mythic dungeon (generally referred to as mythic 0) or by completing someone else’s m+ run (the end of dungeon chest will include a key for you, added to whatever loot you’d normally get)
You will also get a new key every week out of your vault.
That reminds me. There’s no looting in mythic+ like there is in other dungeons. All the loot gets shoved into a treasure chest at the end of the dungeon after the final boss and trash mob requirements are met.
Instead of 2 drops per boss you get two items total between 5 players. It’s personal loot, though, so you don’t have to worry about rolling.