Hi!
1) I've had some firms explicitly say they don't care about the background. Other firms such as White & Case write on their website in a lot of detail about having a good clean background (had to take down my beloved posters). So, I think it's up to the firm. I would go for blurred if your background is not plain as A. it's better to be safe than sorry B. less distractions for the interview = more focus on you.
2) A bit of both. I think naturally you should be able to find something that you are genuinely interested in AND tailors to their key departments since if you are doing an AC for the firm, you should be interested in their key departments. It might be harder to find a crossover but I'd strive to find something. If you can't then I'd go for tailoring it to their key departments and then try and come up with quite a few reasons why it could be interesting and fake it till you make it - but that's obviously risky, they could see right through you.
Just realised that my news story indirectly incorporated a lot of Corporate acquisitions- which is an area the firm excels in
Thank you!!! And sorry to hear about your posters 😅