How can I make an escapeable jail?

An idea to solve your problem with your cells is to make the cell walls out of Obsidian or Bedrock. these should be enough to not be destroyed from the explosion of a Creeper.

This however leave the door, while I can't be say for certain if an Iron Door will be enough you might want to use Lava.

To do this, create a 3x3 square with the middle block empty, this will be a funnel to direct the lava, one you have it facing down the lava will fall straight down, make sure that where it lands you have the block missing so that rather than spreading into the cell it'll just stop.

This has 2 advantages

1. The escapee will get damage as they walk though
2. The escapee will be on fire taking damage slowly for a little while

Both will make them weaker to the creeper's explosion.

Now to have the Lava Fall act as a door, at the mouth of the funnel set up a Sticky Piston move a block in front of the mouth to stop the lava and move it back to reopen it

Lockpicks, under this system, you could use Redstone and have a second Redstone circuit which is broken and if fixed will active the Sticky Piston and block the lava flow, though I have no idea how to do that. and of course you'll need to set up a "window" in the cell to avoid the redstone from being drawn though the lava destroying it (a block on the floor missing so it can be drawn though it rather than the lava door entrance).

Getting Creepers to drop something other than gunpowder you'd probably need a mod or mod the game yourself, same goes for increasing collecting distance.

One possibility would be to use self-repairing walls (basically, a row of cobblestone generators along what-ever wall you want them "escaping" from.)

That way, in your scenario, the creepers blow a hole in the wall, which will then seal up over time (and you can manipulate your redstone circuits to control the speed). Your criminal sneaks out through the wall, leaves, and shortly after the wall is repaired.

You could make the "jail" somewhere high up and with the only exit as a high drop, thus damaging the player on impact. You can even control the amount of damage this way rather precisely, by setting the appropriate fall distance.

I like the idea of Allen Gould however creepers don't engage (and explode) if they can't see the player. If you want to use the self repairing piston wall I suggest TNT strapped to a lever or pressure plate. This however still requires you to recharge the TNT.

If you have access to the /give command and you don't have command blocks disabled you could let command blocks replace the TNT (or simply remove the door for a few seconds before replacing it).

For an actual escape track through the prison, my idea would be to make it parkour like. If you want to make it challenging (and invest a lot of time into this) you could make a speedrun track that if you don't run fast enough (or fail one of the jumps) you can push a button which teleports you back to your prison. This makes it very challenging for the prisoners and extremely frustrating. The buttons once again being hooked up to command blocks. This track will definitely make them think about what they've done wrong.

You could make Zombies guards with little Skeleton "Guardlings" to assist them. Make the walls out of Obsidian with piston doors that automatically close after about 3 seconds (Basic MineSci). You could add Turrets that use pistons so they "slide" and shoot a 2-Infinite line of Fire, but this would take AMMO-HOPPERS to reload, and a lot of redstone to make the Turret shoot. Drowning tanks (cells that drown any player if they step in one) should be present and ready to attack players. Make sure the light level is 0, so it is possible for different mobs to spawn. Change the Gamerule to /gamerule doMobGreifing false, so if you use Creepers, they won't destroy walls. You should add a Passive mob to press Pressure plates which open doors and secret passages (and DEATH) open, so players can get through once the Sheep or something hits the plate. The animal should be in a separate control room. The players, as always, should be on Adventure mode so they cannot break blocks and escape easily. These tips should help out a bit.

You could make a jail with iron doors, and use command blocks to replace anything you don't want to be destroyed. Then, the creeper blows up the door without anything happening to any other blocks.

Make a big box out of bedrock. Don’t forget to surround it with water so they can’t escape with chorus fruit. On top of the ceiling cover it with lava so people can’t glitch through the top with ender pearls.