Yes to all of the above, and that is what most people do do. Usually just have the SSD for the O/S and maybe a few games, and the use the HDD for storage, and programs and games.
However, when you point applications to install to one of the HDD drives intead of the SSD, it might still install some folder and a few files onto the SSD.
Basically, all that you would do is ONLY connect the SSD and then install the O/S.
Then you can hook up the two HDD(s) and install your programs, games, and storage.