This may not be possible but I’m wondering; is it possible to start Linux operating system from a USB drive after the computer already has Windows running? And would the USB drive be swappable so that it could be used on different computers?
An operating system controls the hardware on a computer. It provides the interface between software and hardware. Windows is an OS, and Linux is an OS. You cannot have two competing interfaces for the same hardware.
However, you can run Linux in a virtual machine on Windows. You can run Windows on a virtual machine under Linux. But you have to get the virtual machine up and running first.
And would the USB drive be swappable so that it could be used on different computers?
Yes.