There are two ways you might want to have this work anyway despite namespacing. One option would be that you just import the namespace and get all the stuff in it, this is popular in Java for example, however in C++ this is a bit fraught because while you can import a namespace, you actually get everything from that namespace and all containing namespaces.
Because the C++ standard library defines a huge variety of symbols, if you do this you get almost all of those symbols. Most words you might think of are in fact standard library symbols in C++, std::end, std::move, std::array, and so on. So if you imported all these symbols into your namespace it's easy to accidentally trip yourself, thus it's usual not to do so at all.
Another option would be to have some magic that introduces certain commonly used features, Rust's preludes do this, both generally (having namespaces for the explicit purpose of exporting names you'd often want together) and specifically ("the" standard library prelude for your Edition is automatically injected into all your Rust software by default). C++ could in principle do something like this but it does not.
Leave un-namespaced identifiers to those that are declared in the current file and namespace everything else. If you really want, you’re free to add “using namespace std” or otherwise alias the namespace, but keeping standard library functions out of the global namespace as a default is a good thing! (In any language, not just C++)
You're free to, but I discourage the habit. It's more verbose to add the namespace:: prefix to symbols, but it sure does make it easier on the devs that have to work with the code later.