At the very beginning of the series we learn that the store is on their fourth re-opening. We also learn that the restaurant has been there for at least a few years from the exposition Bob gives us in the opening scene. So, why are they having a grand re-re-re-opening? Because, due to a series of unfortunate accidents, Bob is driven further into insanity and hallucinates each of the children to deal with each accident.
Linda's death is actually what caused Bob to open the restaurant in the first place, years ago, which is why it's located next to the funeral home. Bob, grief stricken, opened the restaurant and began hallucinating Linda. This also explains why Mort frequents the restaurant. He's befriended Bob and checks in on him to make sure he's doing okay. This establishes that Bob is a loving, caring husband, but has trouble letting go and moving on with his life.
After running the restaurant for a few years as a single dad, the restaurant suffers a series of accidents in rapid succession, killing the rest of the Belcher family, leaving Bob alone and hallucinating them in a subconscious effort to return to normalcy and because this was the same coping mechanism his brain used to deal with the death of his wife. The accidents occur in the following order:
1. Fire
2. Rats
3. Telephone pole falls on the storefront
These kill off the children from youngest to oldest. Fire represents Louise, a psychotic who most likely set the fire for whatever reason. Bob actually mentions this in passing when telling Tina that she's the grill cook because he doesn't trust Louise with fire. After her death, Bob starts imagining her, like Linda, but unlike Linda, he imagines Louise with her character flaw, but magnified. She was probably an energetic child when alive that Bob had trouble reeling in, so after death this is the one thing that Bob believes is her defining characteristic. He does this with the other children as well.
Gene dies next. Like Louise starting the fire, Gene caused the rat infestation. During the process of collecting and releasing the rats as a joke, he's bitten and succumbs to infection. Again, Bob reimagines him as a coping mechanism, but focuses on and magnifies his defining characteristic: he's a jokester, but from Bob's perspective his jokes are extremely weird and off-putting. On top of that, Bob imagines him with ADD because, like Louise, he was probably more of a normal, energetic kid, but with Bob's imagination that energy is magnified as well.
Tina is the last to die and her's is the most horrific. She was standing in the window, mopping the floor when the telephone pole crashed through the window, electrocuting her. Bob was cleaning the grill at the end of the day and witnessed her die, but because she was electrocuted, she remained upright and twitching until the emergency responders could arrive. This is why Tina has a thing for zombies. Her personality is completely unlike the other children because she's experienced the deaths of the rest of her family alongside her father. She doesn't understand why Bob continues to act like Linda, Gene, and Louise are still alive and doesn't share in his hallucinations. She also becomes increasingly depressed with each death in the family. She never learns how to cope in a healthy way because all her father does is reimagine the lost family member to avoid moving through the stages of grief. This is why Tina's personality is so flat and so awkward. Bob doesn't understand why she didn't see or interact with the rest of the family, so he assigns her a personality that is very weird and disturbing... again, magnifying it as her defining characteristic. Tina wear glasses because she's the only one in the family to recognize Linda, Gene, and Louise's deaths.
Actually, the first three episodes plainly show that Bob is insane. They all portray how Bob deals with death. The first episode Bob has to experience the hate from Hugo whom Linda turned away in favor of Bob. After learning Bob's restaurant is in his jurisdiction, he shuts the restaurant down with the accusation that they're serving human flesh (symbolizing Hugo holding Bob accountable for Linda's death). The second episode clearly shows Bob is insane... he spends several days in the false walls of the restaurant. This is where Teddy enters the picture. Teddy actually helps run the restaurant and like Mort, tries to help Bob cope to include "seeing" the family. This is why Teddy always looks so tired: he's run ragged looking after Bob. In this episode, he fails a bit as Bob escapes to the false walls, but again indulges Bob's fantasy and lets him stay there. Teddy is actually running the restaurant while Bob is going nuts and calls in Linda's parents to get him out of the wall.
Finally, the third episode deals with Moolissa, the cow that shows Bob feels guilty for the deaths of his wife and kids. In this episode, Bob is shown to begin moving through the stages of grief. He makes remarkable progress throughout the episode, though lapses at the end when Moolissa dies in a near miss accident, almost getting hit by a car. The event triggers Bob's coping mechanism again (he even has a full hallucination and talks to Moolissa while sitting on a pink cloud in heaven).
The rest of the series is actually showing Bob as he moves through the grieving process, which is why we see Bob as the most normal person in the series. We experience the series through Bob's eyes and in it, he believes he's normal.