On the days you workout, you can still use the tredmill, but only for 5 minutes of
light cardio to get to your AT before your workout, and the same for a cool-down after your workout.
As for supplements, you don't really need any to
gain muscle, though some will indeed help. You can do some research on supplements like glutamine and creatine; plenty of threads to search with great info about them. Also remember to take simple carbs with your whey protein, such as dextrose.
Yes, it's a good idea to switch up your program every now and then for variety. Though, switching days you'd work a particular muscle combined with another won't make much of a difference imo, but that's up to opinion. You can benefit by switching exercises, sets, and reps, though.
Yes, do heavy lifting with low reps. Every workout, you should be increasing the weight and making the workout harder than the last time.
Remember to eat enough to support your heavy workouts, and you will build the muscle.