The study I am analysing is a pre-and-post intervention questionnaire of students' views before and after studying a module. The questionnaire was distributed in three different geographical locations, where the same instructor was delivering the same module at different times within one year. The scale used is a 5-point Likert scale (which I can also convert into a binary agree/disagree variable if needed).
The surveys are anonymous, so I can't match the sample. However, in some samples, all the students answered both the pre-and-post questionnaires (same $N$) and in others this was different (different $N$).
Overall I have 343 respondents for the pre-intervention questionnaire, and 378 respondents for the post-intervention questionnaire. However in two of the three locations, I have equal pre and post intervention responses, but they are anonymous: so they are not independent, but not matched. (This is a weakness of the data, and will be reported in the results).
My questions are: a) Given the sample size, would running an unpaired t-test on the full sample be appropriate? Or should I be going for a non-parametric test? b) Can the subsamples where there are equal respondents (i.e. all students answered both pre-and-post questionnaires) be analysed as non-independent non-matched samples?