My fundamental concern is whether in real life when applying to microeconomic theory, we derive the demand curve using utility and indifference curves approach, or we simply may get data on quantity demanded of the consumer for different prices and using linear regression derive the demand curve?
If I understand your question properly, it is correct that we do more ordinary statistical analyses such as linear regression to determine relationships between economic variables (e.g. price and demand.) Utility is a tool which gives us a model of consumer behaviour based on very loose assumptions about how consumers behave (convexity of preferences, monotonicity, etc.) While the demand curve can be derived from utility if we somehow knew the full preferences of all consumers, it can also be approximated from data by observing the real-world relationship between price and demand. It is very difficult/impossible to measure utility in the real world, so using regular statistical techniques like linear regression to estimate the relationship is the logical thing to do.
Of course, the real-world demand curve may not be linear, so a simple linear regression on observed data in the form $p = \beta_0 + \beta_1 q$ may not accurately the demand curve. Here, theory may help you decide on what nonlinear terms you should include in your model, but you would still need to do the regression analysis on real-world data to actually find the parameters.