Hello again bellaru, if you have an opportunity, you may want to get ahold of some books on metallurgy or do some searches on the internet. It is likely that some of this reading may do a better job of explaining what is happening relative to some of the questions that you have. As far as charts go, I don't believe you will find any one chart to give you the kind of explanation that you are looking for. The subject has too many variables and those change with the different materials, alloys of materials, etc. Different types of welding processes can also have a great effect on results of a like material.
     For example, you mentioned arc strikes and the fact that they only take a moment and yet cause all kinds of problems. In the case of the arc strike, the weld metal is at temperature just long enough to melt the electrode and a small amount of the surface metal, it cools this weld metal so quickly that it can cause it to harden considerbly and also cause a shrinkage stress to be present. Then if a bending stress is induced on the surface of the parent material the material from the arc strike won't stretch at the same rate as the parent material and this causes the tearing that willl show up. This is a very simplified version of what is happening. Regards, aevald

bellaru,

Composition, microstructure and manufactured condition, are the contributing factors.
This is not something that can be explained in short as there are books covering this for all the different metals and alloys. But if it can be simplified.

Firstly the steel is made at a steel plant, here they do all the "cake baking" adding ingredients, stirring, removing unwanted elements and then finally casting. Therefore it will have a certain composition and grain structure. Grain structure is difficult to explain to someone that has never encountered it. But just imagine that the steel looks like a honeycomb in the inside. Made up of small "grains" which in turn is made up of a crystal structure which in turn is made up by all the ingredients (elements Fe, C, Mn, Si, Al, Mg, Mo, S, P, etc). The size and composition of these "grains are directly responsible or related to the metal's mechanical properties.
Now, anything in life will always return to the lowest energy state, Humans for instance will rather lie down than run the whole day. The same principles is applied to the grain structure, Elements like to bind in a certain way to reduce the their energy state. If you heat up the steel you supply energy which causes elements to interact and rearrange themselves. If you supply enough energy you will break all bonds and connections and thus you get melting and a liquid, but when you cool the steel down from liquid to solid, you are forcing elements to interact in a solid state. Therefore they will try and be at the lowest possible energy state by arranging in a certain manner/orientation/shape in the crystal structure and subsequent grain structure.
Now this is where time comes in. if you supply energy (heat) you are giving elements which want to move around and rearrange time to do so. The result, grain growth and precipitates (at a high enough temperature) which will change the metal mechanical properties accordingly. This will happen for as long as you apply heat, if you apply it for an infinite length of time it will keep on changing until it is satisfied with its energy state at that temperature.
The thing to understand is that different combinations of composition, temperature and time will give different results. But the unit we are interested now is cooling rate.
It is easiest to explain again from the liquid state or molten metal. If you cool the metal fast you will "trap" elements together in a structure/ arrangement/shape that they are not very happy with, they want to move but they cant because there is not enough energy available (heat) this will cause strain or deformation in the microstructure which in turn will increase the hardness.( in carbon steel this structure is likley to be called martensite)
If you cool it slowly all the elements will move around " diffuse" " substitution" until they are as happy as can be for the time that they are allowed to move around. ( structure is either/combination pearlite, bainite, ferrit etc)

That is why welding and heating is different because you apply different amounts of heat for different amounts of time, which will result in different microstructure. Further in welding you are adding alloying elements which make up for the loss in properties which can be a result of the heating cycle. (various elements in the flux or gas are usually responsible for either/and alloying, grain refiners, deoxidation, wetting, covering/slag etc) The metal will never be like it was initially but in manufacturing all you care about is fitness for service and therefore you do mechanical tests etc. and if that passes you are happy.

I hope this helps and do not add to your confusion. If you do aa search look for CCTT diagrams ( continous cooling time temperature) and Phase diagrams. A good one is the Iron Carbon Equilibrium diagram.

goodluck