In PHP, is there any performance impact on using one long class with a lot of functions in it? Or is it advisable to use many small classes and call them separately when needed?
It's advisable not to think about the performance before you have the code. From the maintainability and understandability viewpoint, of course, smaller classes, with smaller methods are superior. (see The Single Responsibility Principle)
When you need to optimize, you really can assemble (automatically) all your code into a single big file, and save some time on include-s.