You have 61 questions on Ask Ubuntu. I've not looked through all of them, but some of them do demonstrate that you can identify problems.
I haven't looked through them all, but the few I looked at didn't demonstrate the sense of priority or the ability to avoid causing more problems in the process of fixing the one you started out with.
I believe that is to be expected in this format. When you ask a bunch of strangers online, your priority isn't theirs, and it can easily turn some people off if you assert your sense of urgency in the wrong way. While one is panicking, one is very likely to talk like your urgency is theirs if you talk about your urgency at all. Depending on your employer, you may also be on a gag order regarding the urgency or impact of the issue you're asking for help on.
Some of the better answers I've seen do a very good job of explaining some precautions that are likely to be important when applying fixes. I haven't seen if any of yours do, but it's theoretically possible.
Therefore, if you were giving your resume to me, I would at least consider your SE profile in evaluating whether I wanted to call you in for an interview. It's not the best possible show of problem solving skills, but it's something.
If I chose to call you in, I would absolutely make some resume questions out of your SE profile. Finding things to give in depth questions about without probing into things that my employer would expect your past/current employers to have under NDA is frequently a challenge in my interviewing experience, especially if it's a phone interview where the person could consult SE for answers while being interviewed. I mean, one could still come up with questions, but getting the balance right so you don't accidentally disqualify a skilled honest candidate but still disqualifying dishonest candidates is really tough.
But that's me. And I'm not hiring - it's not currently even a likely probability on my potential "other duties as requested" list for the year. Most employers I've interacted with would want to just look at the first page and make a decision from that, and as 520 asserted, that page says nothing about your problem solving.
If you get to talk with the hiring manager before submitting your resume, or someone who knows them, you may benefit from asking about their views on stack exchange. But otherwise, I'd just follow Frank Hopkin's advice, and list it as a hobby.