When to use parametric tests if the data is not normally distributed?

[#1]

Hello

 .If I am investigating a dependent variable that is not normally distributed (Shapiro Wilk p <0.05)

Can I still use parametric tests like linear regression and t-tests knowing that the calculated sample size is 380 and the collected data 1400 (large sample size)

[#2]

There is no assumption by these procedures that the response is normally distributed. The distribution of the residuals is assumed to be normal with a constant mean and variance. The conditional equation applies to the mean, variance, or both.