Explain How to Design Footing in Expansive Soil and What Requirments to a void Problems which Happends- Before & After Design?

first, always to expensive, but: do a good investigation of the soil you are designing on, That's means also you have to know what the maximum and minimum level of the ground water is, If the footing goes deep, see if you have problems with (I think the term is) aquatic water.

The investigation of the soil  and the parameters determines if the deflections are acceptable.

First, increase the depth of incorporation 

Second, replace the expansive soil under the foundations of granular soil gradients selected 

Third, eliminate the risk of water coming into the level of establishing the foundations and lower the water table, if any