Are write sys calls in Linux atomic?

There are a few situations I am curious about learning:

1. Partial writes: If I were to invoke the write(fd, buf, nbytes) syscall, is it possible for only part of the buffer to be written to disk. Suppose the return of write is nbytes which is the same argument passed in, could an inconvenient sudden power loss at the moment of invocation of write() only allow for lesser than nbytes to be written to the disk?

2. If I were to write “This is a cat.” in one invocation to write() and “That is a dog.” in another invocation to write() in a different process to the same file, in what situations could I end up with interleaved output.

3. File appends are supposed to be atomic across concurrent processes if I open in append mode and write lesser than PIPE_BUF bytes per invocation to write(). What about atomicity wrt partial writes. Let us say I have one process writing lesser than PIPE_BUF bytes to a file with one invocation to write(). Could a partial write still occur with the loss of power?

There are some related questions but they don’t provide the full context:

1. What happens if a write system call is called on same file by 2 different processes simultaneously
2. How to safely write to a file?