If the computer who writes the IP packet expects to send it using an ethernet packet, do they always automatically put it in the ethernet packet? Or can someone else do this?

If an IP packet is sent by a program running on a computer whose network connection is through an ethernet, the packet has to be in an ethernet packet before it can leave the computer. So the short answer is yes, the computer automatically puts the IP packet in an ethernet packet.

Within the computer, however, the writing of the IP packet and the putting it in an ethernet packet are performed by separate pieces of software. The IP packet is written/created by an application program like Navigator or NCSA Telnet. The application program asks the machines operating systems (Windows, Unix, MacOS, ...) to deliver the packet. The operating system realizes that the machine's network connection is through an ethernet and therefore puts the IP packet into an ethernet packet before giving it to the ethernet hardware. This way, the application program doesnt have to worry about the type of the actual network connection.