While skydiving we have to jump from the airplane at a certain altitude above Earth. So if for some reason the parachute doesn't open, then will that person (or any object similar to a human body) fall to Earth or will it be incinerated/vanish in the sky due to air-friction in space before coming down to the Earth?
The majority of the heat developed during reentry of a space-vehicle comes from air compression not friction. Remember, to go into space, you don't have to go very high, but to orbit you will have to go very very fast, and it's not the fall that produces the heat, it's the slowing down part.
If you had a human fall without a chute, the terminal velocity (where air resistance cancels gravity and you continue downward at a constant speed) would be around 100-200 mph, not nearly enough to cause any kind of heat (or cars would burn up by going normal cruising speeds). To get higher terminal velocities, you'd have to go a lot higher, where the air is a lot less dense, higher than any skydiver have, and as far as I can tell Felix Baumgartner did not experience any incineration during his jump.
The unfortunate skydiver will almost certainly die, but there'd definitely be a body, and it'll probably be in one piece.
Qualification: I worked at a sport parachute center as an instructor for 10 years and I hold an FAA Master Parachute Rigger certificate. I believe that qualifies me as an expert on the subject.
The fastest a human can fall unassisted is about 300km/h (head-down dive). Far too slow for frictional or compressive heating. Fighter pilots have ejected at supersonic speeds and not warmed up any (it's also rather cold at higher altitudes). You would have to jump from the space station to incinerate yourself.
To answer the primary question, if parachute #1 doesn't open, you use parachute #2. If that doesn't work, you have about 10 seconds left. In consolation, it's not all that messy unless you are unfortunate enough to impact on pavement. An open-coffin service is usually possible.
To reply to other inaccuracies:
the #2 parachute is not spring loaded, the small (1 meter) extraction parachute is.
we don't depend on the
idiot boxauto-activator. There's a handle.
skydiving in pairs is not "recommended" (that's scuba diving). You want to be very far away from other people when deploying parachute #1, and by then it's far too late for anyone else to help. The close-up videos you have seen are carefully planned in advance - the cameraman and subject agree on relative position and sequence, and the video subject deploys his parachute higher than usual. Videos you may have seen of several canopies together are also carefully planned in advance, and it's a lot harder than it looks.
holding someone else during deployment is not possible. No one is strong enough to hang on during deceleration. It's not (normally) a shock but the forces involved are rather substantial. Backup parachutes DO open very quickly - at freefall speeds it's rather unpleasant.
the exceptionally rare cases of someone surviving without a parachute typically involve a steep slope and either deep snow or crushable foliage. Forget water - at 200km/h it's only slightly more forgiving than concrete.
Well, if you skydive in pairs, which as I understand is recommended, and if you catch the error before your partner opens his/her chute, you could signal to them that your equipment is not in working order, and then you could essentially bear hug them while they open their chute.
This is obviously not ideal and could even dislocate the shoulders of the skydiver whose chute did not open.