Simple push button code is invalid, but I can't find what's wrong :(

Does that mean I wrote something in my code wrong (grammatically) that has to do with the particular function?

Yes. Look up how to use a digitalWrite function:-

Now do you actually want a digital write here. It does not return a value so it is odd that you have it on the right of an equals sign.

buttonState1 = digitalWrite (buttonPin1);

Should in fact be:-

buttonState1 = digitalRead (buttonPin1);