Is the Shapiro-Wilk test only applicable to smaller sample sizes? or if it isn't only limited to smaller sample sizes, how is it distinct from applying it on larger sample sizes (>30)?
 A: The Shapiro Wilk test applies at any sample size above $n=2$ (it can't work at $n=1$ or $n=2$). 
However, implementations of the test will generally not cover the very largest sample sizes (such as $n>5000$ -- though if you're using tables rather than a computer to do the test the tables might only go up to say $n=50$ or something like that). 
Such upper limits are for a technical reason to do with the implementation of the test -- specifically the need to obtain a list of constants for each sample size that increases in size with $n$, not because the test itself is in any way unsuitable at very large sample sizes. In principle you could implement it for n=100 million if you wanted to be able to do that. There is no particular distinction between $n>30$ and $n\leq 30$ (any more than there is at any other intermediate sample size).
At very large sample sizes, sometimes people who would like to do a Shapiro-Wilk test will substitute the closely related Shapiro-Francia test for the Shapiro-Wilk (which corresponds to looking at the squared correlation in a Q-Q plot of normality), though at very large sample sizes there's rarely any point in goodness of fit tests anyway (testing random number generators is a plausible application, but outside of that it seems likely to be an unproductive activity).
