Can I create a base template for my project which all apps can draw from? Or do I have to create a base template for each app? And if I wanted them to be the same I'd just copy them?
Sure you can. A quick example of a base.html
<!DOCTYPE html>
<html>
<head>
<title>My Project</title>
</head>
<body>
{% block content %}{% endblock content %}
</body>
</html>
And say you have a app called myapp with a view.html page,
{% extends "base.html" %}
{% block content %}
<h2>Content for My App</h2>
<p>Stuff etc etc.</p>
{% endblock content %}
Take some time to read the docs for more information