Does doing a maths/physics double major give any tangible advantage over just physics? I've read that you encounter a concept in physics quite often before you learn the math to explain such a concept whereas with math/physics double you have already encountered the math to explain the fundamental theory behind the physics concepts as you find them. Is there any element of truth/legitimacy to this?
Not really. I feel like you encounter the math in physics before you see it in math(with the exception of vector calculus and ODEs). However, if you want to do grad physics, I would encourage math because you'll actually understand how the math works and can learn more complex math faster.
Hell yes. If you take a course in Differential Geometry or Smooth Manifolds before you take a course in GR, GR will be infinitely easier.
If you take a course in functional analysis before upper level QM, or even more so QFT, it will also be extremely helpful.
On a more advanced note, taking Abstract Algebra will really help you if you want to go into high-energy physics and/or theoretical particle physics so you can understand the group theoretic construction of the SM and how elementary particles correspond to irreducible representations of the respective lie group.
Are you planning on getting your doctorate in physics or perhaps going to law school to become a patent attorney? If not, I would avoid physics altogether. Not much you can do with it in the real world with a BS in physics that will actually relate to your major.
I'm not familiar with enginnering physics degrees, but if you want to do engineering, you might as well get an engineering degree. You will learn much of the same physics, but you will be able to apply it and know what can be ignored in the real world. I have known many physics majors who have applied for engineering positions who were far smarter than me and failed to get the job while I had no problem getting an engineering job coming out of college with my mediocre grades in an engineering degree.
I don't really think so, at least not at an undergraduate level. If you wanna go deeper into theoretical physics, then yes, more math lectures will be necessary. For the "elementary" stuff you learn it's not massively helpful though.
Look up the video where Feynman explains how the mentality of a physicist is completely opposite from the mentality of a mathematician.
So doing that double major would be like being an atheist and getting a PhD in Theology. Enjoy getting schizophrenia in your early 20s.