According to the DRAE:
5. m. Cada una de las tablas dispuestas horizontalmente en un mueble o en la pared para colocar objetos sobre ellas.
2. f. Estante o placa de madera, cristal u otro material, colocados horizontalmente contra la pared para servir de soporte a algo.
As you have pointed everyone of them matches the definition of shelf provided by the Oxford Dictionary
A flat length of wood or rigid material, attached to a wall or forming part of a piece of furniture, that provides a surface for the storage or display of objects.
But notice that the definition of repisa doesn't mention it as part of a piece of furniture. It usually refers to a shelf directly attached to the wall, la pared. I've never heard that word mentioned as part of a bookshelf (estantería). I tend to identify a repisa also for being made of something different from wood like plaster (escayola) or stone (piedra) but I can't not generalize such distinction to all Spanish speakers.
I'm from Spain so I can not answer the second part of your question. Balda is a common word here, there's nothing strange about it being mentioned in a TV series.