Frequentists tests to check for normality

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Let $X_1,...,X_n\sim X$ be $n$ i.i.d. random variables. I want to to test if they follow a normal distribution, in other words, check if their distribution belongs to the Gaussian family.

These are the tests I'm considering:

  • Kolmogorov-Smirnov test
  • Kolmogorov-Lilliefors test

With these two tests I can statistically test the hypothesis that my data was sampled from a normal distribution. Further tests for univariate normality I've found on wikipedia. I would also like to check for normality visually (with QQ-Plots and histograms), which raises the question,

Is a normal QQ-test a valid way to test for normality?

This question refers to the normal QQ-test, so perhaps someone could confirm if it's legit to use.

And is QQ-Plot the same as a normal QQ-test or am I confusing concepts here?