1) You do not need to learn the PHP framework, and in fact, if this is the first website that you have ever built, I would suggest creating it without a framework to understand how PHP works when creating a website. This way you understand things like database connections, session management, etc., which are often done behind the scenes using frameworks. Then later try creating it using the framework to get an idea of ββthe design patterns and other functions that the built-in environment has in order to avoid repeating code, security holes, etc.
2) I do not know what the difference is between AJAX + some PHP and just PHP + some javascript. AJAX is part of Javascript, it is not a separate technology in itself.
Some websites use a lot of AJAX, some do not. It really depends on what you want to do on the website and your particular design: AJAX can provide a smoother experience, but it can be difficult when it comes to things like back buttons and bookmarks.
3) Depends on what you do with the framework: if you use only 10% of the functions, you certainly will not become a master at any time. It also depends on the complexity of the structure: I did not use Zend, but I know that the more complex the structure, the longer you will need to study it.
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