Why is the Sun so bright, but you can feel it far away? First of all, the Sun's surface temperature is only about 6000 K. Years ago I was working at at a melt work with furnace temperatures 0f about 2-3000 K; of course you could not be near a furnace without protection, when it was open, but you could still stay some 20-30 metres away from it. Likewise, a light bulb has no long reach, till it fades away. But how about the Sun? Why can experience it at 150 000 000 km away? 

Besides, I wonder why space is not heated up, because the heat radiating from all the stars and galaxies is so enormous, and actually the matter density in space is so low. How, actually, can heat be absorbed in space? What temperature is measured in space - is it just the wavelengths of radiations, from which temperature is calculated?
The answer to your first question has to do with luminosity. It's a measure of power, the energy given off by an object in a certain amount of time, which you can think of as brightness. The more luminous the object, the brighter it appears.

We can treat the Sun as an idealized object called a black body, which emits thermal radiation according to something called the Stefan-Boltzmann law. Assuming the Sun is spherical, with a radius $R$ and temperature $T$, then its luminosity $L$ is
$$L=4\pi\sigma R^2T^4$$
where $\sigma$ is the Stefan-Boltzmann constant. The important thing here is that $L\propto R^2$. If the Sun was the size of one of your furnaces, it would not be very bright; if the furnace was spherical and could be treated as a black body, the two would have the same luminosity.

The Sun, however, has a radius on the order of about $7\times10^8$ meters. I don't know how big the furnace is, but I'm assuming it can't be larger than ten meters, to an order of magnitude. First, that's a size difference of about $10^7$. Second, we square the radius when determining luminosity, meaning that there's a difference of a factor of $10^{14}$. To make this a bit more meaningful, the Sun is then essentially one hundred million million times more luminous than the furnace, even though the temperatures are the same.

I feel like your second question may be a duplicate of What is the temperature of outerspace? (see also the questions linked therein), and Run like hell has already tried to address it. barrycarter's comment, though, is spot-on. The flux from the source, $F$, drops off via the inverse-square law - that is, at a distance $r$ from the source,
$$F\propto\frac{1}{r^2}$$
Remember how we just established the power (pun intended) of squaring a large quantity? Interstellar distances are enormous; the nearest star system, Alpha Centauri, is roughly $10^{16}$ meters away, or ten thousand million million meters. Now square that distance. That's a tiny factor - even when multiplied by the luminosity of all three stars, which combined is still on the same order of magnitude as the Sun.