I heard somewhere that the second law of thermodynamics is stating that some heat (energy) becomes unusable for work (at the scale of the whole universe). Why is it like that? Can't heat be converted into some energy forms? I do understand that entropy is the measure of spontaneity, but I am having hard time understanding this.
How can we depict heat in relativistic (classical) level and quantum level? Is there heat energy that is not mediated by any form of particle?
Actually heat is indeed usable as you state, but we should understand what it really means.
Heat is a way in which energy is transfered from one system to another. The other way is work. When we say that we use heat to produce work, we are making a conversion from one of these energy forms to the other. To do that, a differential in temperatures is necessary, otherwise no heat transfer can happen and much less work can be done.
The problem is that at some point, after transfering heat from temperature reservoir to ever lower temperature reservoirs, your heat becomes so dissipated, i.e. the temperature so low that you can't find lower temperature reservoirs anymore to continue dissipating the heat even more in the hope of producing some more work.
To use a bit of a different picture, think of a watermill. What drives the watermill to produce work is the height difference. Now, you say, once the water has gone through the mill, let's just put another mill below it. And after that one, another mill. But clearly, there must be an end to that process. So it is with heat.
I don't know about your second question though. I'll just say this, heat is the macroscopic result of work at a microscopic level that does not result in work at the macroscopic level. For instance, when heat gets transfered from a hot bucket to a cold bucket by contact, all that really happens is either the molecules mixing through each other or the molecules colliding and exchanging energy. Work does happen, but it's at the microscopic level between colliding molecules and not at the macrolevel in the sense that the buckets move or the water moves or something like that. Maybe that clears up your second question.
So, the quantum level explanation of heat is not really markedly different from a classical level explanation assuming molecules. The details of the microscopic processes are different, but they are not really relevant to the macroscopic process, unless maybe you look at quantum processes that have some macroscopic consequences.
There's an analogy based on viewing heat as a liquid e.g. water. You need to be a bit cautious with this as like all analogies it fails if pushed too far, but I think it helps with your question.
Anyhow, if heat is like water then temperature is like water pressure. If you have water at different pressures you can use the water to do work. This is how hydroelectric power stations work. But as you generate electricity from your power station the water flows from the high point to the low point, and eventually it will all be at the same level. Once this happens you can't get any work out of it because there's nothing to make the water flow. For a hydroelectric power station rainfall refills the upper reservoir, but for the universe as a whole once the heat is uniformly distributed that's it - there is nothing left to move the heat around so you can't extract any more work.
Re the second part of your question: suppose we have some heat (e.g. by burning coal) and we use this heat in a steam engine to pump water from a low point to a high point. Some of the heat has been turned into the potential energy of the water so in this sense the heat has been stored in a form that doesn't rely on particle motion.
Heat is just a form of energy, and all forms of energy are interchangable, though rarely (if ever) with 100% efficiency.