Reason behind the decomposition of price effect into substitution and income effects
Why are we decomposing the effect of a change in price of one commodity into all these effects which are (as I have understood), all hypothetical.


They're hypothetical, but they are nevertheless meaningful.  We can easily imagine what it would be like if an agent had a larger budget while prices remain unchanged; we can also imagine what it would be like if, under diminishing marginal utility assumptions, the relative prices of goods were to change.  

One reason we do this is that it helps develop intuition and show why naive assumptions don't necessarily hold.  For example, if we have goods $x$ and $y$, prices $p_x$ and $p_y$ with budget $B$ in an initial equilibrium, we might naively think that setting $p_x^{'} = 0.5p_x$ means that we consume twice as much of $x$, when this is not the case for most utility functions.  


  Also in substitution effect, why do we substitute the relatively less expensive commodity for the relatively more expensive commodity? Is there any particular advantage of this decomposition?


The answer to the second question is that the Slutsky decomposition allows us to tell a story that answers the first question - when the price of $x$ falls, we may buy more of $x$ (an income effect), but we will also buy more of $y$ because diminishing marginal utilities implies that after using the price-savings to buy some number of additional units of $x$, we get more "bang for the buck" by purchasing an additional unit of $y$ instead.  This is the substitution effect.


  Also I don't exactly understand the meaning of real income.


Real income is income adjusted for inflation from a base year, so that it reflects real purchasing power. In the context of these Econ 101 budget-line models, it's implied that the budget is in real units for pedagogical reasons. There's no base year, but the point is to ensure that any price-changes contemplated are "real", and to get you to think of consumption as the basic economic unit, rather than money per se. Often you'll see simplifications where one of the goods is priced at $1/unit, and referred to as the "numeraire".