No.
No.
No. Lots of people get jobs with a BA in philosophy. Especially with work experience. And philosophy has one of the highest salary growth potentials of any major, including the sciences and engineering.
You can, of course, teach yourself how to code. You could also go to a boot camp. You can even get a job by teaching yourself how to code or going to a boot camp. However, as someone who works at a tech company, I will say that there is a difference between someone who can write code and someone who is a software developer. Software developers do so much more than just write code; there’s more about computer science you need to understand to be a good developer. So take that into consideration.
Before you decide what to do (and spend money), I encourage you to actually talk to some folks who are doing jobs that you’d like to do. Reach out to some software developers with different kinds of backgrounds - some with a traditional CS major; some who taught themselves or did a boot camp or majored in something besides CS in college. Do an informational interview and ask them about their experiences. You can find them through alumni networks at your school or by reaching out on LinkedIn. You’ll hear lots of different answers and opinions, but through hearing from multiple people you may get a decent idea of what the better path for you is to the kind of job you want in the field.
I don’t think you need a BS in CS to do an MS, but I do think you need some formal coursework/prerequisites in CS.