Sudden gap between disc brake and pads? I had adjusted my disc brakes (Tektro Spyre-C) in such way that the gap between discs and pads were tiny (just enough to slide a sheet of paper). 

Recently when I rode through a forest, there was a heavy rain and the front disc started ringing and creaking. The latter could be the effect of sand, the first one -- a cone? I took a look but because of the rain I could not see a thing. I figured out I pull the lever gently and wipe out anything that is stuck around the disc.

It worked. Too well. After a while I realized I had to pull the brake lever up to the handlebar to stop. When I get to home I noticed the gaps between disc and pads are much bigger.

I removed the pads now, they look ok (the contact/braking surface is around 2mm thick on both), the spring which separates them also looks healthy, I don't see I lost something, so now I wonder what happened? If I a not mistaken to make the gap bigger the only way is to adjust the screws which set the initial position of the pads.

Unless the pads were skewed in some way when I bought the bike and this rough ride "fixed" them. But then how it is possible for pads to be skewed in the first place and if it is a case why all (around 1500 km) braking so far didn't show or fix this?

Can anyone tell what could be the problem? Or what problem I have now I am not aware of? I am asking about it as well, because all I see is to do is to put pads back and adjust the screws to have a gap tiny again.
It sounds like what probably happened is you did the kind of ride where the brakes are exposed to enough wet grittiness that significant pad material is lost over the course of one ride. This is also kind of the hallmark disadvantage of organic pads, if that's what you have. The 3mm pad adjusters primarily exist to compensate for pad wear, so that's what you should be doing to narrow the gap again. The idea is that eventually when the pads are all the way worn, you can then screw them back out and not have to adjust anything else for the new pads.

Another element to this can be that any initial error in parrallelism between the pads and the rotor will also result in the gap widening quickly as they break in and wear into a more parallel state, which you would also use the adjusters to correct. Some amount of this is inevitable although you want to avoid it as much as possible with good initial adjustment and prep. It's unlikely you experienced much of this here unless those first 1500km were somehow in very mild conditions without much need for the brakes.