Is NASA planning a mission to Mars?
Yes, NASA is planning to go to Mars, but no date has been set, nor does there exist at present any development effort to go to Mars. Reason: Shortage of funds.
How does the space shuttle handle the heat of reentry?
Objects entering the Earth's atmosphere travel at very high speeds. As they pass through the atmosphere, they heat up due to two factors: 1. They compress the air on their leading edges (i.e., the sides in the direction of motion). 2. There is friction with the air. This heating makes the objects glow. Depending on the size and the kind of material they are made of, objects may burn up completely or they may burn up only partially. They may also break up.
For instance, interplanetary dust and chunks of debris arrive at Earth at speeds in excess of 25,000 miles/hr. When the microscopic dust specks burn up we see shooting stars. Larger chunks sometimes reach the ground. We call them meteorites. There are meteorites on display in many natural history museums.
The space shuttle enters the atmosphere at speeds somewhat less than 17,000 miles/hr. On its nose cone and the leading edges of the wings, as well as on its underside, the shuttle is covered with ceramic tiles which can withstand the heat that is generated during reentry and can protect the craft and crew.
Incidentally, rapidly flying aircraft also get hot when they travel near the speed of sound or faster. They are made of special alloys (in the case of the SR-71 it's titanium) that can withstand the heat. But they don't get hot enough to require the thermal protection of tiles.