Rooting allows deeper access to the system, but unrooted android can do many things you need to jailbreak an iPhone for.
You can install free apps anyway. If you mean installing paid apps for free that would be illegal and forum rules forbid discussion of it.
You almost certainly can improve performance with the customisations that rooting makes possible.
I'd suggest visiting the Galaxy Note All Things Root forum to learn more. Rooting is different for different devices, so it's best to speak to people who know your device.