Very nice position to be in - congrats! :-)
To answer your questions:
1. I don't know about BCG but McKinsey got through the crisis exceptionally well. They will hire more people this year than ever before (official statement of their global recruiting lead), and more specifically for Germany, they are recruiting heavily + former colleagues and friends are all staffed with full utilization rate.
2. From a business perspective I think the impact was mostly affecting the media coverage, not so much the actual daily operations. The firm would not hire as many people this year if there were serious concerns (since they operate very conservatively with staff projections) and clients still flock to hire McK. There are two news outlets (NYT and Manager Magazin), which constantly hit on McKinsey. I explained this in some answer here a couple of months ago. McK operates highly decentralized with several 1000s of projects ongoing at the same time. There will always be bad apples, however, I believe that they are dealing with this phenomenon now + this does not affect 99.999% of the other projects.
3. I have no insights into that
4. I have never had more down-to-earth, warmer, and funnier colleagues. There was never any competitiveness in the team room or elsewhere. That might be relevant if you are talking about going from AP to Partner level to a certain degree because there is a huge bottleneck after 6-8 years in your career because not everyone can become a partner. Everyone can become EM and almost everyone can become AP (if they meet the bar, which depends on collaboration, not competition). In fact, the mindset I learned was rather 'let me help you be successful, so you can help me be successful.
5. Left just before COVID started, so I cannot really tell. I know that everyone is always working on work-life balance in consulting. How effective these measures are I am not sure since at the end of the day client will most likely always be the priority.
Additional point: McKinsey offers a better support system that covers a lot of things outside of your core work (slide generation, help desk that solves every problem for you in Excel, PPT that would take more than 5 minutes to solve for you, etc.). This is a huge lifestyle improver, which I have not heard from in discussions with BCG colleagues. Lastly, McK has a global staffing model, which makes it easier to travel the world while you work.
What helped me decide back then was the interactions I had with everyone during recruiting events, during the interview process, and afterward. I solely based my decision on the feeling and vibe I had with the people of both firms + the global staffing model
All the best with your decision!