Why is the rice in the mushroom risotto always very hard

Agreed, scaling up sauces that require reduction can be tricky, but it actually reduces to a simple physics problem. First I'm going to give you the best solution and then the science behind it.

The solution is to use a larger, shallower pan and apply higher heat, while stirring more frequently. I usually go a quarter step up in heat on the stove; so, from medium-low I go to medium, and from medium to medium-high. Using your stove's ventilation fans may also help. If you're doubling the amount of liquid you reduce, you can assume roughly a 50% increase in time required to reduce it, following this advice. Normally, it would require doubling the time to reduce the sauce.

And no, you cannot reduce the amount of liquid... if you double the recipe you need to double the liquid too. The liquid is reduced to add flavor and body to your sauce. Doubling the spices and other ingredients without doubling wine and stock will yield a sauce that is too spicy, lacking in depth, and does not have enough volume. Alternately, if you double the stock and wine but do not reduce enough, you'll get a watery, bland sauce, because stock adds gelatin, which thickens the sauce.

If there's meat cooking in your reducing sauce: reduce the sauce until it needs only the suggested time to finish reducing, then cut the burner to the suggested power and cook for the suggested time. Using a higher temperature setting will overcook the meat, making it tough. Also, using a partially reduced sauce will impart more flavor to the meat; since the flavors are already somewhat concentrated before adding the meat, more will penetrate the meat. If this is a problem, break your recipe into normal sized batches and cook them on separate burners.

If you're concerned about estimated the right amount of time for a doubled recipe, you can reduce in the specified way before adding meat, then add meat and do it again.

Now the scientific explanation:

The principal problem here is the rate of evaporation. Let's break it down!

Liquid needs a lot of extra energy to transition from liquid to vapor, called the enthalpy of vaporization. For water, the energy required is 6 times what it took to heat it to the boiling point from room temperature. Once it hits the boiling point, it can't get much hotter until the liquid is almost completely gone. This means the rate of evaporation is mainly limited by hot fast you can input heat.

The rate of heat input is limited by the power supplied to the burner, but a second limit comes from the pan; the rate of heat transfer is proportional to surface area, thermal conductivity, and the temperature difference between two surfaces. Turning up the burner gets it hotter, increasing heat transfer, but the pot still needs to transfer that heat to a liquid, so using a broader and more conductive pot exposes more liquid to the heat. It also distributes the heat over a wider area, preventing the liquid from overheating as easily where it touches the pot. Stirring ensures the heat is evenly distributed, maximizing heat transfer (by increasing the temperature differential) and preventing over heating.

Evaporation is also impeded by a pressure and a high concentration of vapor above the surface. This concentration will be higher if there is liquid has less surface area (the same amount of liquid released into a smaller volume). So, the liquid out in a bigger pot increases the evaporation rate. The local concentration will be also higher if humidity is high (more water vapor in the air), and higher if there are no air currents to disperse the vapor boiling off. So, running vent fans and using a shallower pot will make it easier for the vapors to escape. A ventilation fan may also slightly reduce pressure, but that has more to do with weather. In industrial food processing, a vacuum may be used to evaporate liquids at a much lower temperature than normal. For example, this is how powdered and evaporated milk are made.

Finally, in a tall pot, escaping vapor may lose heat to the cooler walls of the pot as it rises, re-condensing and falling back down into the pot. If the pot is lidding, this is even more of a problem. For this reason, it is advisable to use an open, un-lidded pot. This effect can be used to evaporate away alcohol from a sauce while retaining the water content.

So, to double the rate of evaporation and maintain a constant reduction time, double the power supplied to the burner, and increase the surface area of the pot. Of course, you often can't double the burner power without burning the liquid... so you're left with using a larger pot and increasing the heat as much as you think you can get away with. If you stir enough and scrape the pot's sides down, you can get away with quite a bit.

As I understand it, it's down to the flavour you get from frying the rice. However, it does also break down some of the starch which reduces the thickening it can do when the risotto cooks, which might cause a problem. I can attest to the flavour, but I've not done experiments about thickening.

Serious Eats had a good article on the topic though, in which such experiments were described. The solution in that was to wash the rice in the stock, then fry the rice, then add the stock containing all that undamaged free rice starch during cooking, thus giving you toasty flavour and creamy risotto with no questions asked. I haven't tried that, but it seems like a fairly sound idea to me.

http://www.seriouseats.com/2011/10/the-food-lab-the-science-of-risotto.html