Yes, since I started the project, I’ve had a work system in mind that would let you earn more money. However, it’s quite an ambitious mechanic and requires time to implement properly. That’s why I decided not to include it in this first public version.
Don't worry about the AI it's just a first version, so progressing in the project has zero impact. As for the other issue, what necklace are you talking about? You don't need any necklace to advance in the main storyline at least as far as I remember.
In the game, you level up by pressing the exclamation mark on your phone. When you level up, you receive one social point and one skill point. Additionally, you gain experience from working, but only if you have already reached a new level beforehand.