I am sorry for your loss and my late entry to the thread. From the outset, I'm going to be brutally honest here, because that's how we look at these things as professionals. As hobbit1983 pointed out, you may have to explain the extenuating circumstances. However, to an outside observer, that explains one or two of your retakes. It doesn't necessarily explain or excuse all of it.
Why do I say that? When I was a Check Pilot, I had a few cases where the person I was examining had just lost a family member that morning, or they were heading out from the check to say goodbye to a loved one. The one pilot told me about their loss before the check, so I canceled the ride on their behalf. No ride, no result, no consequences. They showed up to the check because the only flight out to be with their family was later that evening, and they didn't want to inconvenience the company. The other pilot did not tell me ahead of time. They were preoccupied and failed as a result. They explained the situation afterward, but unfortunately, once a test begins, that's it - the result stands, my hands are tied the moment we finish the briefing. I've had numerous other instances where pilots had just broken up or got divorced that week, their child was in the hospital, or any number of other serious family emergencies. So I'm not at all suggesting that the loss of a family member is not a significant issue - it is the highest stressor from a human factors standpoint. However, continuing to press on when you know you are in a position akin to incapacitation is not always a sign of strength or high morals. It can be a sign of poor decision-making or personal awareness. It is only ever up to you to take a step back and ask yourself how something is affecting you. Although I would ask before every check ride "Is there any reason, personal or professional, that you think we should talk about before the ride or any reason we should not go forward with the ride today", it is ultimately up to each of us to answer that question honestly, and know when it is time to bow out for a day, a week, a month, or whatever time is necessary to safely continue on.
Someone, somewhere, may ask why you thought it was a good idea to continue your training when you were very obviously distracted. They will ask as it is germane to the flight deck. From their standpoint, your decision may force another pilot into a single-pilot scenario through your decision to show up to work when you should have called in. As long as you can answer this question with honesty, integrity, and a plan to avoid it in the future, you'll be good.
Now, the other opportunity you have here is to look for any common issues in your exams and the flight test. Stress always puts a spotlight on your best and worst qualities and knowledge, and you have a bit of data to work with. Go back through your exam results. What did you get right or do right and what did you do or get wrong? Are there any similarities in the subject matter? Only you can answer that, but take those positives and negatives, and relate it to operational flying. How could a lack of knowledge become an issue for you during an equally stressful situation in flight, and how can you minimize the effect going forward? Alternatively, what did you do right and how can you build upon that so that it becomes more of a strength during a stressful situation? These again may be questions that you'll be asked and that you want to have an answer to. Any in-flight emergency is stressful, and how we handle that stress is the #1 difference between pilots and non-pilots. You've got a great opportunity here to develop as a person and as a pilot. Don't waste it thinking about what airline XYZ will think. Fix it and be ready to answer their questions, but ultimately, screw them. If an airline can't handle a person who has learned from their experiences, then you don't want to work there anyways.
In conclusion, I know lots of pilots who failed exams or flight tests. I twice failed the NZ CPL nav and air law exams, and it didn't do anything to my career because I took stock of what went wrong and why and carried on. I've also been in a position to fail pilots during a check ride who then took that experience, ran with it, and became some of the best airline instructors I've had the pleasure of working with. These failures won't define you unless you let them. And while you have a valid reason for some of those failures, so do lots of others, so you can't completely use it as a crutch; so don't.
Best of luck in your future.