Why unit impulse function is used to find impulse response of an LTI system?
It is important to realize that due to the LTI property the response to an impulse $\delta(n)$ describes the system completely, because any input signal can be written as a weighted sum of shifted impulses:

$$x(n)=\sum_kx(k)\delta(n-k)\tag{1}$$

Let $\mathcal{T}\{\cdot\}$ denote the system operator, so the response to a shifted impulse is

$$\mathcal{T}\{\delta(n-k)\}=h(n-k)\tag{2}$$

From (1) and (2), due the linearity and the time- (shift-)invariance of the system, the response to any input signal $x(n)$ can be written as a weighted sum of responses to shifted impulses:

$$y(n)=\mathcal{T}\{x(n)\}=\sum_kx(k)\mathcal{T}\{\delta(n-k)\}=
\sum_kx(k)h(n-k)$$

This last equality is the convolution sum describing the input-output relation of a discrete LTI system.