With a Likert scale, respondents indicate their standing on an item along a quantitative continuum, e.g., 1 to 5 with a 5-point scale. Multiple items are summed or averaged to gain a total score for each person. Both descriptive (e.g., means and standard deviations) and inferential statistics can be used with these scales.

Of course they can be statistically processed to produce the composite measure (overall score), which then can be used as a variable in addition to your other variables, then you will indeed use statistical procedure to analyze your variables

Yes! They can be used as dependent variable (in an ordered probit/logit model, for example) or explanatory (becoming a set of dummys for veryhigh/high/medium/..)

I appreciate the comments. Thank you.

Yes, because the Likert scale is designed to transform quality into quantities.

Likert scale measurements take advantage of the concept of Random Variables by assigning numbers to intangible statements or attitudinal statements. As my colleagues here mention , quantitatively you can use descriptive statistics and causal research to dig further into the data.

Good Luck.

Dear Susan, hope this link works for you.

https://methods.sagepub.com/reference/encyclopedia-of-survey-research-methods/n273.xml