Does overclocking increase the heat/noise a GPU produces?

Heat - yes
Noise - yes, since fanspeeds need to be higher to remove the extra heat
Shorten lifespan - yes, how much depends on how high the overclock
Void the warranty - yes, if you tell them you overclocked the card

Assuming you keep the temperatures at the same level that they are from factory, then it won't shorten the lifespan, at least in theory. To do so, the fan speed must be increased, causing more noise.

It does void the warranty, but if you change it back to stock speeds, there's not really any way of telling if it's been overclocked.