$key_length is the number of output bytes that you desire from PBKDF2. (Note that if key_length is more than the number of output bytes of the hash algorithm, the process is repeated twice, slowing down that hashing perhaps more than you desire. SHA256 gives 32 bytes of output, for example, so asking for 33 bytes will take roughly twice as long as asking for 32.)
The doubling of the length that you mention is because the code converts the output bytes to hexadecimal (i.e. 2 characters per 1 byte) unless you specify $raw_output = true. The test vectors included specify $raw_output = false, since hexadecimal is simply easier to work with and post online. Depending on how you are storing the data in your application, you can decide if you want to store the results as hex, base64, or just raw binary data.