1)
I wouldn't focus too much on a particular practice area - after all, your exposure to the wide range of practice areas at this stage will be very little and it's best to keep an open mind (no one really knows which practice areas they'll enjoy and want to qualify into until they start their TC). However, there's nothing wrong with showing an interest in a particular practice area and relating that to the firm's expertise - this can be a good way for you to illustrate commercial awareness and an understanding of what the law firm does (by explaining why you are interested in that area and linking it to the firm, e.g. via a recent deal/award).
Type of training is quite common but can be a good one - especially if the firm is known for not pigeon-holing its trainees and having a small trainee intake (typically giving you the opportunity to gain more responsibility at an earlier stage within a more collegial atmosphere/culture). Make sure to be specific at every step and explain why that appeals to you.
Diversity can be an acceptable humanising add-on, but make sure you can relate it to your experiences and that it's something the firm actually cares about (and I wouldn't personally write as much about diversity as I would for the other reasons).
I also second what D.Cole wrote above - particularly about naming a specific person from the firm that you met at a networking event/careers fair etc.
2)
What do you mean by agile working? If you mean more flexible working conditions (working from home etc), I guess you could relate that to the firm's culture/emphasis of providing a happy working environment and thus improving the productivity of its lawyers (and thus the competitiveness of the firm).
I'd scour the firm's website and look for how they themselves sell themselves to potential clients, and try to find some recent initiatives the firm has taken (such as investment in AI or blockchain technologies etc) and link that to the firm investing in being able to provide a full-service and competitively-priced service to clients of the future etc.
(There is no necessarily wrong answer, as long as your points are logical, well-founded, relate to the firm specifically and are well-articulated and expounded upon then that will do.)