I'm not a teacher, for transparency, but I have been involved in education as a governor for many years until recently, so used to regularly interview for staff, and I work in the public sector. I think you have had an unfortunate culture clash between sectors, in part, as well as a lack of research.
'How to you respond to feedback' was an open ended question, designed to allow you to show your reflective ability to accept constructive criticism and build on it for future work. To show that you can develop as a teacher, work in a team, and that you'll cooperate with your assigned mentor. That you don't think you're a done deal. You tried to assure your interviewers that you are fully used to feedback from all directions, but your answer implies a 'been there, done that, move on' attitude, which shuts down further discussion.
Saying you need the bursary, as a reason for why now, is a bit daft. The bursaries aren't going anywhere, really, and you make yourself sound like you're just looking for a stepping stone. You must have other reasons why you want to teach? You must have other reasons why now is a good time? Even if it was as simple as "I've enjoyed a career in X, but when I was at LSE, I enjoyed learning languages so much that I want to pass on that love of languages to other young people. I feel that I am at a stage in my life where I have the maturity and motivation to dedicate my time and energy to teaching, and my experience in X field will help me because ....."
I don't think the questions you were asked were common sense or straightforward, either, btw. They were all asked to elicit your soft skills. So yes, you have 3 languages, you will probably be able to deliver the curriculum, but will you be able to come alongside children and open up their world? Will you be able to talk to them? Reach them? Make them passionate about languages? See when they are at risk or in trouble? Safeguarding is a role for every teacher - would you notice, would you care? Those sorts of questions are trying to pick that information out, so they aren't common sense, at all, and there are wrong answers. There are lots and lots of right answers, and people answer them in very different ways. But there definitely are wrong answers, and they are noted, and they will fail an interview.