I have known about PC speakers to give beep codes, and some people use them to play music. Does this exist in a laptop? If not, what would happen if a program tries to use the PC speaker?

 

Laptops have capable sound cards/modules and are frequently used to play music and speech. The internal speakers are generally moving coil rather than piezo ones, AFAIK. The headphone output can be used to drive an external amplifier and speakers for better sound quality.

 

The generic speaker device provided by the operating system is simulated and played through the sound card and speakers.

 

Yes
Some of the miniature speakers are remarkable thanks to mobile phone development.
Some are smaller than the size of a fingernail.
Not quite HiFi, but not bad either.
The microphones are just as remarkable.