<backtab> is called a "function key", but it can be bound to a command in any keymap. (Forget about function-key-map in this context.)

Vanilla Emacs (emacs -Q, no init file) binds some function keys in various keymaps. And libraries you load can do so too.

Work from the modes that are current at a given time, in any context. Use C-h k to find out what such a key is bound to. Determine what keymap it is bound in (probably a mode keymap), and then unbind it from that map (in your init file, on the mode hook, for example).

You can see the keys that are currently bound in a given keymap using C-h M-k (describe-keymap) followed by a variable bound to a keymap (or followed by an actual keymap, if there is no variable). You need library help-fns+.el if you want to use describe-keymap.

(But I do wonder why, other than for learning about keys and keymaps (which is a good thing), you are undertaking this exercise of removing key bindings. More typical is simply binding a different key to the command whose binding you don't like. Anyway, I don't need to understand why.)

Maybe I can answer part of your question(s). Others can probably help more here.

<backtab> is called a "function key", but it can be bound to a command in any keymap. (Forget about function-key-map in this context.)

Vanilla Emacs (emacs -Q, no init file) binds some function keys in various keymaps. And libraries you load can do so too.

If you really want to remove function-key bindings, I'd suggest that you work from the modes that are current at a given time, in any given context. Use C-h k to find out what such a key is bound to. Determine what keymap it is bound in (typically a mode keymap), and then unbind it from that map (in your init file, on the mode hook, for example). Rinse and repeat.

You can see the keys that are currently bound in a given keymap using C-h M-k (describe-keymap) followed by a variable bound to a keymap (or followed by an actual keymap, if there is no variable). You need library help-fns+.el if you want to use describe-keymap.

Some function keys (such as backtab and f1, or rather <backtab> and <f1> (but I prefer naked notation) are pretty standard. Others are specific to Emacs. You can think of a function key as a logical name for something that can have different physical implementations. backtab is typically essentially S-TAB, for example. This is what is behind the "translation" indication you sometimes see in *Help* for C-h k.

(But I do wonder why, other than for learning about keys and keymaps (which is a good thing), you are undertaking this exercise of removing key bindings. More typical is simply binding a different key to the command whose binding you don't like. Anyway, I don't need to understand why.)