jQuery is regular javascript. It is a js library, meaning nothing but that it is a collection of js functions in an object. Hence, going with your terminology, yes, it can be mixed.
That being said, calling jQuery.noConflict(); is superfluous, since the library supplied by wordpress is loaded in noConflict mode anyway.
If something inside your jQuery(document).ready(function() {...} does not work as expected, there is most likely an issue with that code itsself.
You could edit that into your question and might get help here, but seeing that you have an account at stackoverflow as well, it might be a better idea to ask js/jQuery questions not specific to wordpress there.
To round this up: while you can declare nested functions in js, it would be good practice to declare them locally and thus keeping them out of the global namespace like so:
jQuery(document).ready(function() {
var yourFunc = function() {
// do something
};
yourFunc();
});