Recommendations - so here’s a rundown.
Required (3): 1 counselor and 2 academic teachers (Junior or Senior year) - so yes, it’s mandatory.
Strongly Recommended (1): peer recommendation
Other (2): arts teacher if submitting an arts portfolio; additional recommendation from somebody that does not fit into any of the other categories (e.g. coach, employer, etc.)
Here’s the link with the information:
https://admissions.dartmouth.edu/apply/choose-your-path/regular-decision/recommendations
I understand your predicament re:A-levels. I know that some schools will allow you to submit recommendations from an O-level academic teacher. With that said, you should contact the admissions office directly and find out what they will or will not accept. I know they have to be from academic teachers though. The admissions office get plenty of applicants from England, so I’m sure they’ve answered this question before.
As for Diversity Club, if it’s really important to you, by all means you should include it. Nonetheless, it’s often helpful to first think about the story (narrative) that you are going to tell in your application. Then think about how your EC’s reflect that and determine which ones provide the strongest evidence or support. The various parts of your application should all work together.