I want certain keys and key combinations to behave as other keys or key combinations in Emacs. For example, I want F5 to behave as a substitute for C-c for every possible combination involving it, or C-S- as C-. Is it possible to do that without manually rebinding all such key combinations?
The keys you are referring to are known as 'prefix keys'. A prefix key has its own keymap, so to make another key behave the same, you need to assign it to the same keymap. For control-c, you use the mode-specific-map:
(global-set-key (kbd "<f5>") mode-specific-map)
Control on its own isn't a prefix key, or really a key at all, since it doesn't send a keypress to Emacs[1] until you hit another key. I'm not sure how to remap C-S- to C- within Emacs. You could do it system-wide with xmodmap, but that's probably not what you want.
[1] the control key (and shift, alt) do send a keypress to the operating system, but Emacs doesn't 'see' this unless there's another key pressed at the same time