What materials is the heat shield made out of?
A number of different materials. Recommended reading:
http://en.wikipedia.org/wiki/Space_Shuttle_TPS
Why does the nose sustain such high temperatures? What makes the nose so special?
The nose is the point where most of the hypersonic air flow is divided to flow around the shuttle. The shock wave is most intense at this point and hence receives the highest heat flux. The effect also occurs along the wing leading edges, which is why the nose cap and wing leading edges are made of reinforced carbon-carbon.
How does the heat shield work? Does it absorb heat? Disperse it like a radiator? How?
See above link. It absorbs heat and later re-radiates it. See also:
http://en.wikipedia.org/wiki/Atmospheric_reentry#Thermal_soak
And, last one: What would happen if the next shuttle docked to ISS, then it was discovered that the Heat Shield had a crack in it and wouldn't be able to survive re-entry? What would happen to the shuttle and its crew?
The crew would stay on board the ISS until a rescue flight (called Launch On Need) can be flown. The maximum time before exhausting ISS consumables is about 80 days. See:
http://en.wikipedia.org/wiki/STS-3XX
I'm not positive about all but the last. 2 missions ago, when the shuttle went to HST, there was, for the first time, a backup shuttle. If tiles were damaged, the shuttle would not have enough fuel to make it to the ISS.
That would be STS-125, slated to be launched in Oct 08. It did not launch and has been delayed until May 09:
http://www.nasaspaceflight.com/2008/10/atlantis-de-stack-hst-spare-hardware/
All flights since the Columbia accident have had a "backup shuttle" but STS-125 was the first to have the backup on the pad ready to launch within 7 days of call up (the delay is about 40 days for a normal Launch On Need mission).
Question is, what would happen to the shuttle? Perhaps repair if possible? The problem with HST is that there may not be enough time for a repair.
If it was deemed too dangerous to return the crew, a repair would not be attempted. For ISS missions, if there was a reasonable chance of the orbiter surviving reentry (but too dangerous for the crew), it could be flown to Edwards by remote control. For STS-125, or other ISS missions where the damage was likely destroy the vehicle, it would be re-entered tail first over the Pacific to ensure breakup in uninhabited areas.
If the heat shield is cracked the crew can go out with a special gun with a special material that can cover it and make it as good as new.
They can make it good enough, but not good as new
. And only for damage of limited size.
