i'm aware of very few engineering and physics programs for undergrads. FSU has a computer science program though. several places have math courses: number theory, complex analysis, differential equations, etc.
i suspect a lot of schools cover calc and ODEs in about 70 weeks. a bit less than 15 pages per week.
i take notes while reading; this is necessary as some of my books are borrowed. you could also try some video lectures to add an audio-visual component.
exactly. as humans we see everything in terms of our world, observations from our solar system, etc. i think this stuff is largely beyond 21st century science.