1) No - I only think you should include things where you don’t meet the criteria. This goes for extenuating circumstances more generally. If you have performed strongly, there is no need to mention the circumstances.
2) You don’t have to describe what the organisation does in a work experience entry no matter how long it is. You should just focus on your responsibilities, the outcomes from your work, and if there is anything you particularly gained from the experience.
3) You’d only provide this information if asked to describe careers events you have attended. If the firm does ask for this, then you could just combine the programme of events you attended with
Linklaters rather than listing them one by one. If it’s obvious what you learnt from the title, then don’t mention it again. It’s only if it’s something that isn’t obvious that you should.
4) Yes - culture can be assessed by not meeting the firm in person.
5) You provide examples to back up your claims of these three skills. It doesn’t matter if it’s one example, three separate ones, or even more. It’s just about substantiating your claim of them. It doesn’t matter what the examples are though.
6) Personal referees should not be relatives. They should be someone who has known you for a long time who can verify who you are and vouch for your character. Ideally they should be in some form of professional role (civil servant, nurse, teacher, small business owner, middle management in a company, anyone with professional accreditations for their industry).