What you refer of using just $a instead of $_GET['a'] (or $_POST['a'] too) is an old feature known as register_globals. This feature was dangerous and leading to messy code, so it was considered deprecated in PHP 5.3 and finally removed in PHP 5.4.
Then, using $_GET['a'] everywhere in your scripts may lead to problems, because you should never trust user input (all things coming from $_GET, $_POST, $_REQUEST, $_COOKIE and some from $_FILES or $_SERVER). It is recommended to do something like $a = sanitize($_GET['a']); (the sanitize function does not exist, depending on what type of value are you expecting, you should check that what you get is an integer, or a valid date, or whatever, depending on your needs). From now on you should stop referencing $_GET['a'] and use instead the new sanitized variable you have just created $a. Because if you were using always $_GET['a'], chances are that you forget to sanitize it someplace.
Also, before sending this sanitized variable into a SQL query, you should escape it or use it inside a prepared statement to avoid SQL injections. Before outputting it to an html for the user to see, use htmlspecialchars to avoid XSS attacks.
And finally, about having multiple php blocks mixed with html blocks, this is only bad for maintenance reasons, because in the long run it will be a complete mess. Try to separate the html you send the user from the php code. Try to read something about the MVC pattern (Model-View-Controller) (this link is probably too complicated or maybe you don't see the utility right now for you that are just beginning with php (at least I didn't see how it was way better than mixing html with php, for all the complexity needed), but try to grasp the idea behind it) .