Question 1: How do you explain in your tenure file/narrative about research projects that you've stopped working on? This could be perhaps that a manuscript was rejected, maybe even more than once, or it's just a project that's not going anywhere. This is especially a concern at schools that have lower publication requirements, where one missing project could be a real blight on your record.
Answer 1a: I always tell my doctoral students: “Don’t be like me: Don’t not publish your dissertation.” The only part of my dissertation I published was the literature review. I still think I had a solid dissertation (and so did my committee), but I also got tired of submitting it and getting it rejected (and felt like it was because a lot of the reviewers didn’t understand my econometric analytical model). Since I’d started new research projects and was having more luck with those, it made it easier to give up on publishing my dissertation data and findings. I agree with the advice that if you have a “red flag” in your promotion/tenure record, that you need to directly address it (using as little space as possible so as not to overblow it), and move on. So, for example, in my file I could have said (I can’t remember how/if I handled it with this statement: “Unfortunately, I never published from my dissertation data after discouraging reviews from peer-reviewers. Fortunately, I have had far more success with my post-dissertation research projects and have been able to produce a tenure-worthy record of publications.” Someone else I know had the great misfortune to have no significant findings in her dissertation, a highly quantitative model. I always argue when I’ve taught methods that variables being nonsignificant are still findings, but journals often don’t find them so interesting. This person could have a research statement that read: “I had the misfortune of having no significant findings in my dissertation research, which resulted in difficulty in publishing from my dissertation. Therefore I started/continued other research projects….”
Answer 1b: I would be upfront: “My interests have moved in a different direction and I believe that the time that I can devote to my research is best spent on more promising avenues of inquiry.” Then I would go on to explain why X, Y, and Z have ignited my passion and intellectual curiosity and I determined it was more efficacious for my promotion prospects to focus on these projects.