1 - If something falls apart, it breaks into pieces because it is old or badly made.
2 - If an organization or system falls apart, it becomes disorganized or unable to work effectively, or breaks up into its different parts.
3 - If you say that someone is falling apart, you mean that they are becoming emotionally disturbed and are unable to think calmly or to deal with the difficult or unpleasant situation that they are in.
Ex1: "The work was never finished and bit by bit the building fell apart."
Ex2: "I guess it was like that for you when your company started to fall apart."
Ex3: "I was falling apart. I wasn't getting any sleep."
An expression used to indicate that someone is making a big deal out of nothing. Stolen from a line of dialogue in a bad movie, Tommy Wiseau's "The Room".
Megan: So, Will. We need to talk. It may not be important to you, but the cap on a toothpaste tube should have a tight seal. If it does not, then bacteria can manifest itself in the paste, not to mention the cap coming off and squirting toothpaste onto my clothes.
Will: (holding his head in his hands and screaming) You're tearing me apart, Lisa!