Or you could just use some software to create Compose keys or Dead keys on your keyboard, and that wouldn't prevent you from using Ctrl-A.

As for the more complex things, there are certainly also pieces of software that do macros via hotkey, AutoHotkey being one of them. (You didn't investigate it very thoroughly.) They also often have built-in functions for doing mouse actions, including AutoHotkey.

FWIW, even if you could generate a left click with your keyboard, it would click wherever your mouse happened to be, not on the item you intended to click on. And you can do mouse clicks with your keyboard. You just need to turn on MouseKeys.

The advantage to all of this is that you don't have to reprogram your keyboard and get yourself stuck when trying to log in.