Can the Arduino handle lots of variables?

Your arrays look perfect.

Variables take space from SRAM, and the chip has a limited amount of SRAM available. (See the main Arduino reference page for your model's SRAM size.)

An int is bigger than a byte. If your variable always falls within the range of 0 ~ 255, you can use a byte instead, and save the difference in space. Code will likely run a little faster, as well.

I hope this isn't throwing even more advanced ideas on top of your newfound understanding of arrays, but I think this is also a good time to learn about structures of variables.

I have no idea what you're doing with all these buttons or potentiometers, but I'll jot down a few bits and pieces of a program that uses an array of structures to organize similar data.

struct aButton {
    byte pin;
    byte val;
    byte state;
    byte check;
};

aButton buttons[11];

void setup() {
    ...
    buttons[3].pin = 8;
    buttons[3].val = 0;
    ...
}

void loop() {
    ...
    for (int i = 0; i < 11; i++)
        if (digitalRead(buttons[i].pin) != buttons[i].val)
            do_something_with_button(i);
    ...
}