Does applying standard normalisation lead to normal distribution? Does applying standard normalisation to data variables mean changing the distribution of data variables to normal distribution having mean=0 and variance=1?
 A: Take any sample $(x_i)$, subtract the empirical mean $m$ and divide by the empirical standard deviation $s$ to obtain $(\widetilde{x}_i)$:
$$ \widetilde{x}_i := \frac{x_i-m}{s}. $$
Then $(\widetilde{x}_i)$ will have mean 1 and standard deviation 1 (so its variance will also be 1).
However, it will not be normally distributed. The normal distribution is the familiar "bell shape", and the standard normal has the "bell" of a particular width (the variance) and at a particular place (the mean). Not every distribution with the same center and the same width automatically has the correct "bell" shape. Standardization shifts and scales a distribution; it does not change its shape.
For instance, here is a histogram of Poisson distributed variables with parameter $\lambda=\ln 2$, and its standardization as per above. The standardized variables have mean 0 and variance 1, but they are certainly not normally distributed. Note how the bars of the histograms have different width; this is a consequence of the scaling.

R code:
set.seed(1)
xx <- rpois(1e4,log(2))
xx_tilde <- (xx-mean(xx))/sd(xx)
opar <- par(mfrow=c(1,2))
    hist(xx,breaks=seq(-.5,max(xx)+.5),col="gray",xlim=c(-2,7))
    hist(xx_tilde,col="gray",xlim=c(-2,7),
        breaks=seq(min(xx_tilde)-sd(xx)/2,max(xx_tilde)+sd(xx),by=mean(diff(unique(xx_tilde)))))
par(opar)


There is no "normalization" of data. There is no way you can take a given sample $x$ and change it in a meaningful way to something that is normally distributed in general. If your original data are lognormal, you can take logarithms and end up with normally distributed data. (If you want, you can then standardize it as above to end up with a standard normal distribution.) But if you start off with a general distribution, the best you can do is generate normally distributed random numbers that are in some way "inspired" by $x$. For an illustration, look at different beta distributions. These are confined to a finite interval (the normal distribution lives on the entire real line), they can be symmetric or asymmetric, they can be uni- or bimodal.
