If I want try use KDE Plasma instead of GNOME and install it as second desktop on already configured and working Ubuntu 18.04, will I be able to run/use all the old programs installed with (GNOME) Ubuntu Software using KDE environment OS login?
In short, nothing will happen with your already installed gnome applications. They will continue to work as before.
In Linux, different desktops can be installed on a single system. And indeed, each user on the system can by default long in on his/her favorite desktop.
All existing applications will remain available for all users of the system, along with the new applications that came with that new desktop. All applications can be used on any desktop, although the use of different themes and widgets may cause an application look a bit out of place when run on a different desktop than that for what is is primarily designed.
All users will see many applications in their menu system, including these that belong to another desktop environment and that they probably will never use. This can be seen as a disadvantage of installing multiple desktops on the same system. While undesired applications can be hidden in the user's menu on a per-user basis, this requires manual editing of the launchers, or of the menu when a menu-editing application is used.
Another potential issue is that different desktops come with different graphical login managers or screens. In Ubuntu, the current display manager will be replaced if another desktop is added using the *-desktop package. For example, the system will have a KDE login screen after the KDE desktop has been added to the system. A sufficiently skilled system administrator, however, can control what display manager is used for login, and actually may proceed to a more granular install, selectively installing these packages that are desired on the system.
With respect to memory use, there are no immediate consequences of having an additional desktop installed. Memory use depends on the applications you effectively use, not on the amount of software installed on your hard disk. In general, more memory is required if you use programs based on different toolkits simultaneously, because the libraries for these different toolkits need to be loaded in memory. That, however, is independent on having one or more desktops installed. It will also happen on a system containing only one desktop, for example Gnome, if you want to run a KDE application, example KDEnlive.