Yes, a legal education will help in these ways, but so too will training in mathematics. One question not always asked is whether one actually wants to do what law school is the prerequisite for: law practice. I strongly suggest the work of Morten Lund in this area. He's written three books on the realities of law practice. They're short, and a (very) real-world look at what law school leads to. I know everyone nags about reading this or that, but Lund's books really are important to see. If you read those and still agree, you're in much better position to carry on. If not, it's a cheap lesson.
If I go back to law school, then I am going to be geared towards starting my own private practice. Law firm, shmall firm. Big law, shmig law. I think it's about private practice. But maybe that's just me. And I agree, math helps. You know what? I got an A in Pre-Calculus, Calculus I, and Calculus II before taking the LSAT or going to law school. I wonder if that helped me more than getting a 166 on the LSAT and then going to Gould School of Law at USC. You want to know why? Well, my theory is that everything is a machine and I postulate that in order to use a machine you must know calculus.