Are threads copied when calling fork?
No.
Threads are not copied on fork(). POSIX specification says (emphasize is mine):
fork - create a new process
A process shall be created with a single thread. If a multi-threaded process calls fork(), the new process shall contain a replica of the calling thread and its entire address space, possibly including the states of mutexes and other resources. Consequently, to avoid errors, the child process may only execute async-signal-safe operations until such time as one of the exec functions is called.
To circumvent this problem, there exists a pthread_atfork() function to help.
The child process is created with a single thread—the one that called fork(). The entire virtual address space of the parent is replicated in the child, including the states of mutexes, condition variables, and other pthreads objects; the use of pthread_atfork(3) may be helpful for dealing with problems that this can cause.
From The Open Group Base Specifications Issue 7, 2018 edition's fork:
A process shall be created with a single thread. If a multi-threaded process calls fork(), the new process shall contain a replica of the calling thread and its entire address space, possibly including the states of mutexes and other resources. Consequently, to avoid errors, the child process may only execute async-signal-safe operations until such time as one of the exec functions is called.
When the application calls fork() from a signal handler and any of the fork handlers registered by pthread_atfork() calls a function that is not async-signal-safe, the behavior is undefined.