Comparison of two treatments (paired and unpaired)

Hi all!

I'm working on my Master thesis and need to make sure I'm not doing it wrong.

My research:
Are answers to questions a and b significantly different from one another, and why?
Questions a and b are answered on a scale from 0 to 10.

My data:
153 survey responses, split into 3 treatments (1 with question a, 1 with question b and 1 with questions a and b)

447 survey responses with questions a and b (but slightly different background questions)

My problem:
I have compared a and b in separate samples with t-tests and Mann-Whitney ranksum.
I have also compared a and b in the paired sample with t-tests and Wilcoxon signed rank.

The data is neither normally distributed nor symmetric - most people reply in one extreme of the scale, and most (375 out of 447) picked 10 for both a and b.

Now, I don't see the point of doing ANOVA, since the problem really only concerns two questions. Is there anything else I can do to compare these samples?

In addition to this, I'm doing some ordered probit, probit and chi-square to see the relationship between different answers and background questions. This should be relatively straightforward.

Thank you very much in advance for your help!