Humans surviving in space
One would not, under normal conditions, die within seconds. This is a common trope in science fiction, but there has been quite a bit of real research into the subject.

Let's speak on each point.


The extreme cold


This isn't really a huge problem. Space isn't necessarily cold. The extraordinarily low density of matter in space means that the movement of energy through induction is extremely limited. If one were to step into 'space' one wouldn't feel cold, or even cool.  For engineers, often the greater problem is not how to deal with cold, but how to deal with heat, as even though one can't easily release heat through induction, one can certainly gain it through radiation or internal chemical processes.

A person, however, is likely to experience cooling due to the process of liquids in the body evaporating and escaping, taking some of their heat with them. It's unlikely that this would prove fatal though, or at least it's unlikely to be the first thing to prove fatal.


The Intense Radiation


Radiation is a problem in space, but it's not going to kill you so quickly.


  During a 360-day round trip, an astronaut would receive a dose of about 662 millisieverts (mSv), according to RAD measurements. National space agencies limit exposure to about 1000 mSv or less during an astronaut's entire career; NASA's limit corresponds to a 3% risk of exposure-induced death from cancer. (Kerr, 1031)


Currently, orbital missions get some protection from radiation as they are within the Earth's magnetic field, but for those travelling beyond this there isn't a lot of protection. Part of the reason is that things that provide good protection are also very heavy, which can be quite difficult in the economies of reaching escape velocity. As such, one wouldn't necessarily be exposed to that much more radiation outside of a shuttle or their suit in space than they would otherwise.


The Vacuum


This is where things can get messy, but there has been some research on the subject. Obviously one can't breath in a vacuum, in fact the lungs actually begin to dump oxygen, essentially working in reverse due to the lack of air pressure. Our victim is likely to lose consciousness within 10-15 seconds. If they happen to be holding their breath when they become exposed, the pressure difference could cause some real damage to their lungs.

People often theorize that blood would boil in space. Geoffrey Landis disagrees with this on his blog, in which he speaks on this subject. I highly recommend reading through it as I would consider him both thorough and authoritative on the subject. 

I couldn't find the official report, but there are frequent references to a 1965 (Earth based) pressurization incident, in which a technician's suit depressurized within a chamber. He remarked afterwords that the last thing he recalled before blacking out was feeling his saliva begin to boil on his tongue.

While your blood arguably won't boil, you would experience the boiling of other liquids in your body, water particularly.  This can result in rapid swelling of the body. While not pretty, this isn't likely to kill you. However, nitrogen can also become gaseous due to this, potentially resulting the bends, a condition more closely associated with pressure differences in diving. This condition could prove fatal, but AFAIK there hasn't been a lot of research into this in reference to vacuum exposure (This condition tends to become dangerous during the return to normal pressures).

All of this can be survived, as long as pressure is returned relatively quickly. Within a minute is probably enough to save a person's life with little lasting damage. After 2-3 minutes, it's likely too late. The difficulty is that the unfortunate victim may be able to survive 1-2 minutes of exposure, they really only get 10-15 seconds to do something about the problem. Of those who have survived vacuum pressurization incidents, their survival is mostly credited to the quick thinking of those around them.



To respond to your more specific questions:


Exposure for half of what would generally be fatal


This could vary a lot, like depending on whether they were holding their breath. However, generally it's believed that a person could recover from this with little to no permanent damage. Probably the biggest risks are lung damage due to pressure differences, the bends and other related complications, and brain damage due to oxygen deprivation.


Exposure to space that wouldn't result in imminent or eventual death


A little exposure without other complications will generally be survivable. We don't have a ton of data on the subject, so it's possible that unpredictable complications could arise, and frankly it's not exactly advisable, especially considering the person will lose consciousness quite quickly.


Partial exposure


I can't really rely on any specific source for this, but presumably exposure of an extremity would be perfectly survivable. I'm not quite sure how this would work as it would be very difficult to partially expose someone to a vacuum. The human body isn't exactly leak proof. In theory, you would begin to exhibit symptoms in the exposed body part, but you would remain conscious (assuming your respiratory system isn't exposed) and generally be in control of what's going on. Eventually other complications would likely set in and need to be managed carefully.


Exposed to space from inside a room with a single open door


As noted the radiation and temperature is not terribly dangerous, but with no way to repressurize the room this can quickly turn fatal. The Russian Soyuz II mission ended catastrophically when the capsule carrying the cosmonauts depressurized on way for reentry, killing all three crew members on board.  A valve malfunctioned during the reentry, causing depressurization. The craft was recovered after reentry and had not taken any significant damage. It was believed that Patsayev had made attempts to fix the valve in order to save the crew, but unfortunately there was simply too little time to accomplish this. Initial reports suggested that the crew had died of asphyxiation, however autopsies showed that the cause was hemorrhaging in the brain - reportedly caused by oxygen and nitrogen in the blood boiling. Not sure how this works out with Landis's claim that blood does not boil.

Radiation Will Make Astronauts' Trip to Mars Even Riskier
Richard A. Kerr
Science 31 May 2013: 340 (6136), 1031. [DOI:10.1126/science.340.6136.1031]