You have many questions, so it's probably clearest to answer them in turn:
Q: Do I compare a segment with another segment or compare a segment with the overall sample (without segmentation)? Which statistical test can I use for that?
A: What would you do if you were comparing means of rating scales here? If your hypothesis is that Segment A differs from Segment B, then that's a two group test and you run it as an independent groups t-test. If your hypothesis is that Segment A is different from the total sample then it's A vs total sample, but then you have to use a t-test that corrects for the partial overlap in your samples. If it's that Segment A is different from the non-A parts of the sample, then it's a two-group independent t-test again. If you want to know if there are any differences among segments A, B, C, D then you could run an ANOVA for the omnibus test and follow up with post hoc tests appropriate for ANOVA.
Your remaining questions to be answered in comments below for clarity.