In my field (psychology) and probably others, it is common practice to treat the sum or average score across a set of unidimensional items as a "quasi-continuous" (metrical) variable and apply methods for continuous outcomes such as linear regression, ANOVA, and path analysis. In many situations, this is probably fine, especially when the sum or average score is based on many items and when its distribution approximates a normal distribution. You could still use methods that use robust standard errors and test statistics to be on the safe side (e.g., robust maximum likelihood estimation or bootstrapping in path analysis and structural equation modeling).

If you wanted to go a step further, you might consider conducting an IRT or ordinal factor analysis first and work with the metrical IRT or factor scores derived from those analyses. However, in many situations these more sophisticated scores will be very highly correlated with conventional sum or average scores.

Before you create a scale, you should evaluate the extent to which all your items do indeed measure the same thing. The most basic assessment for this is coefficient alpha (with desired value of at least .7). Beyond that, you could conduct an exploratory factor analysis (principal axis factoring with oblique rotation).

Likert scale data should be considered ordinal. In which case mean is not appropriate as that is for continuous data. Wouldn't you consider no of counts in each category, then use a statistic to compare with factors or other continuous variables.