No. Whether to use a switch statement or a series of if statements will become abundantly clear when you understand what each does. If you are not comfortable with the switch statement, nothing it does can not be done with a series of if/else if/else statements.
The converse is not necessarily true.
Then I don't understand what is wrong with the code I have written. Am I exceeding the limitations of the capabilities of the arduino or something? I think I have a pretty good idea what a switch statement does from reading this: switch...case - Arduino Reference and the previous majenko link, but is there a more important difference that isn't stated here? Like from what I understand of the language, my code should work, but when I run the device it just locks up. It seems the delays are a problem (?), something about interrupts (which I don't really know anything about) but I see how switch statements (or if statements) could be used to work around those and (I guess?) work around the interrupts? Perhaps I should write a new code implementing some of these things, see if that works, and if it doesn't come back here again and ask about more specific fixes?