He should separate the med school and the university link in his mind, UNLESS it’s the state where he has residency. Fwiw, technically speaking, all med schools are ‘solid’! In-state med schools are one of the best bets in terms of both admissions and cost. What is your state?
Pretty much any college will be near a hospital for shadowing- and more. For example, University of Richmond, which is an LAC (and offers 25 full merit scholarships) not only has shadowing but a program for pre-meds that gets them EMT certified as student, so they aren’t just shadowing- they are doing.
Also, " He really wants pre-med too and if that is the case he needs to get some REALLY good grades and go to a “semi” prestigious school" is only half right. Any top 200 school will be more than good enough to get into med school- the cuts are made on GPA & MCAT, then LoRs, PS, and some experience elements.
Re: SAT/ACT: half of our collegekids intuitively ‘got’ the SAT, the other half ‘got’ the ACT, so it is a good idea to try both! (there are some standard tips on prepping for the ACT online). Ours arrived in the US having never taken a standardized test, and it is a bit of an art! They also had the same out-of-order problems adjusting to math as you are describing. Khan Academy or a good tutor is your friend here!
From your posts it sounds as though the best thing you can do for him is to help him find a way to graduate from college debt-free, and put any extra money you had set aside for college towards med school. So: instate publics are your first port of call followed by named scholarships (both college sponsored and others). Improving the SAT/ACT could help save tens of thousands of dollars, so worth spending some time on over the summer 