Hey, thanks for playing and being so invested, means a lot! :)
Unfortunately, the softlock when you give Mikey an item is a bug that we found too late to fix for the jam.
Fortunately, you can still finish the game:
!!!SPOILER HINT AHEAD!!!
You're actually missing one major item. Try speaking to Janet again after she rejects you the first time, if you had already spoke to Yasna about Frank (the game should remember it from your previous runs if you did). Janet might have something to convince Frank, if you don't make her angry with your answers.
Also, the softlock bug with Mikey only happens if the time transfer kills him when you give him the milk or rat, so if you take the milk or cheese and rats quickly and run to Mikey, he will survive and you will not get softlocked.
!!!END OF SPOILER HINT!!!
Let me know if you manage to finish it. I hope you will enjoy the ending :)