when filling in the work experience section, it it necessary to include ALL work experience we've ever had?
I would not say so. I think it is important to select the ones you feel are more relevant and that shaped your professional persona if that makes sense. When I was applying I had many internships and experiences I could have discussed but I ended up choosing a certain number firstly because the application does not allow you to put more than 6 or 7 sometimes, secondly because some of them I felt would have not helped like others in explaining my diverse skillset.
Something I would also consider going off of my last point above is to select experiences that are able to showcase a diverse skillset that you can bring to the role of a trainee solicitor like attention to detail, communication skills, advocacy, written skills etc.. I feel like as long as you include work experiences that demonstrates all these skills and more, your selection will be effective in portraying an holistic picture of you.