You are not guaranteed to stay army when switching from Infantry to Med Tech. Med Tech is a purple trade, so it can be any element. I know of one infanteer who is now an Air Force medic and another who was armoured and is now navy. Depends on what the military needs. In the past I was told the military likes to have 60% army, 20% air and 20% navy. These percentages may have changed in the last few years.
On Pat Platoon, if you do not wish to live in shacks, you can write a memo through your CoC requesting permission to live off base. Again, no guarantees. You may still be required to maintain a bed space in the shacks for inspections etc. You can also apply to do OJT/OJE at your home city if there is a base nearby. I was lucky enough to get to go home during 6 of the 9 month wait for my course. Others filled their time doing driver wheel courses and being patients for the med students.
Hope that answers some of your questions.