A gate allows signals above a certain threshold to go through, while completely blocking anything below the threshold. There are several uses for it. For example when recording a particularly noisy source, it's good to put a gate to block out the noise when the instrument isn't playing. Another reason is to control bleed (for example when micing drums).
A limiter is basically an compressor with an infinite ratio. It's used to prevent peaks passing a certain set point, usually as a final step in mastering where by controlling the peaks, it allows you to raise the average volume of the mix.