Say you're in a space capsule. The space capsule has mostly survived re-entry, but the capsule's parachutes fell off. If you had a regular skydiving parachute with you, is there any way you could skydive and survive? Would you even be able to open the door? When should you jump?
Would you even be able to open the door?
It would depend on the capsule, but since the Apollo 1 fire, one expects crewed American capsules to have explosively-jettisoned hatches that can be activated by the crew.
If you had a regular skydiving parachute with you, is there any way you could skydive and survive?
Yes. Terminal velocity for falling capsules isn't particularly high, so in general it should be possible to blow the hatch, jump free, and skydive to safety. As @notovny notes, this was how the first couple of Soviet Vostok flights ended, although they had the benefit of a rocket powered ejection seat to clear the capsule.
When should you jump?
High enough to ensure that your parachute has time to fully deploy, but otherwise as low as is practical -- the capsule will be moving slower due to resistance from denser air, and you'll be less likely to get hurt on your way out the hatchway. The Apollo capsule's drogue chutes were supposed to automatically deploy at around 7km altitude, and the main chutes somewhere below 3km, which is low for recreational skydiving, so you probably want to get out as soon as you realize the mains have failed.
Note that capsule parachute failure is rare. The 1967 Soyuz 1 accident is, as far as I know, the only fatal parachute failure in spaceflight thus far. One of the Apollos had one of its 3 main chutes fail to deploy correctly, resulting in a hard landing but no serious injury.
The Red Bull Stratos jump was done from about 39km up (high altitude balloon). It was fairly straightforward, in that he jumped and opened a parachute. His max speed was just above mach 1 (800mph/1300kpm roughly) and when he moved himself from the freefall to a more traditional skydive position, he was at a more tolerable 500mph/700kph. By the time he reaches 10,000ft he's just barely at 125mph/200kph. Parachute opens at 9000ft. BBC video linked, but the Red Bull site above has one with mission data in-lined (like SpaceX does)
The catch here is assuming the capsule isn't tumbling out of control. If so, good luck trying to get the door open (even with explosive bolts, you have to reach the switch), let alone getting yourself out. If it's just free-falling, you should be able to do what Stratos did and merely jump with an appropriate parachute.
The other catch is making sure you orient yourself to open the chute. If you start tumbling, it could be game over.
I don't see anyone mention here the aspect of heat.
You say from a space capsule, but don't state a maximum altitude. To use a capsule, I assume you mean above the atmosphere. This means on reentry heat would be an issue. The friction of the atmosphere on the jumper as they decelerate from frictionless travel and orbital maintenance speeds.
This is an interesting article on it.
The question would be, say they jumped from geostationary orbit. Unlikely, but just say. They'd need to decelerate just to reenter. As a non vehicle they'd have little space for fuel, but little mass. Could they even carry enough fuel to reduce speed enough for a warm reentry when they hit the atmosphere. I'd say no...
I'd say this is probably the limiting factor rather than much else... The speed required for altitude maintenance, vs fuel for deceleration and how much can be carried, to keep the reentry within the temperature requirements AND limit the yaw forces excerpted on the body as you hit the gases in the upper atmosphere. These might be more dangerous!
The balloon works, because it is in essence stationary. There are limits to that technology, from orbit would be very different.