How to analyze a variable measured on a Likert scale and its interaction with another

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I have to analyze this variable which consists of scores given to 3 items (1-9 scale). This "likert scale" measures "brand commitment" if thats important.

1) Firstly, should I compute 1 new variable that combines the 3 statements (they measure the same latent construct) in order to make it analysable? I understood that calculating the mean is not always the best way - is there something better for the situation?

2) Secondly and most importantly, I want to analyze how this variable interacts with one of the factors(IVs) from my experiment. I ran an ANOVA to test my previous hypoteses. However for this case, putting a likert scale in the ANOVA is considered controversial by some people. So is it appropriate to use ANOVA for a likert scale (if so - should the variable have some specific levels)? If not can you suggest some other parametric or non-parametic method that is suitable for analysis of this interaction.

Any help is appreciated. Thank you.