1. I probably don't care. On the list of things I want from a shell (what you are asking for isn't a function of the terminal, but of the program running in it) this is so low, I would never cared if it was added. I never wanted it to work like this, but as long as it doesn't actively get in the way, I'm OK with it.
2. What's "normal"? Do you mean CUA-style navigation? In that case, absolutely, no effing way! These keybindings are awful. And it's good that they are awful. It wouldn't be a good idea to often accidentally press C-c and kill whatever thing you are working with. But, it's not a convenient key chord for an operation as common as "copy". Now, you may say "in addition to already existing text editing key bindings": but then, again, no, because I want these keys for rare and dangerous operations. I don't want them to be duplicates of existing and better functionality.
NB. Both of your improvements aren't about terminals. They are about programs run by terminals (eg. shells). But you probably knew that already. I realize that OP and the comments lump all these tools together under the same label. But it's still worth pointing out that these are separate issues at least in the sense that nothing you can do to the terminal will effect the change you want to see.