Will I get denied admission to the new school if I don’t have taken their requirements(required courses)?
The school has its own policies.
Generally, the school will evaluate transfer credits to see if they fulfill any requirements. The school shouldn’t expect all of the required courses to be completed–they know you still have to complete their core curriculum. However, if you’re talking about prerequisites, that’s a different story. They may still admit you, but not having the right prerequisites will stop you from taking upper-level courses.
So I don’t really have to care that much about prerequisites if I am desparate to transfer? Get that figured out once I get there? (Fyi money is not the problem)
Each of your target institutions sets it own policies about this. You need to ask each of them separately. It really, truly, is OK for you to do that.