You should install python and the rest dependencies on the host system to build target image!
This message was posted on behalf of Intel Corporation
How you install packages would depend on what you'd like to install. I mean, if the package is on the opkg repos for Edison, then it the simpler procedure would be for you to set the repo if it's not set up already and install it with opkg, as you mentioned. But if the package is not on the repos, then you have two main options, build the package from source or build your own image that includes the package. Of the two options mentioned, the one that is usually simpler is to build the package from source, however, there are exceptions and in those exceptions (I can't remember any at the time, but I have definitely experienced them) it is a lot easier to build the package into the image using the BSP.
If you'd like to learn more about how to set up the repos or how to add packages into the image, then I'd suggest you read the following documents: