Thanks for the review! We did consider saving key progress between deaths, but decided against it because we did want there to be some kind of stakes and challenge. When you die, the tiles reset (otherwise we'd have to add another way to reset the level if you accidentally made it unplayable). So if the keys don't reset, then you don't have to find a solution that works to get all the keys; you just have to find a solution for each key individually since your key progress is restored when you die. We might develop this more after the jam, and if we do then we could add a sandbox mode so you can play with the mechanics.
As for the fire, I did realize after making it that its use was limited. But here's a fun fact that might help you make better use of it: fire doesn't spread to empty tiles, which means if you cut off the fire (for example, by using the beam tool (#2)), you can limit the area it affects.