Thanks a lot for the analysis!
There is a checkpoint system: every time you accept a new contract, the game saves (it is written below the Accept button). Restarting from the first room might've been confusing to you, but you were indeed in possession of all the keys and weapons you collected up to that point. Even your contract is the very same as it were when you agreed to it.
Again, thanks for the feedback! Let me know if you'll give the game another go!