1. Does it make sense to take a shot at the IVY league schools?
First thing I think you need to do is adjust your school selection. There are a plethora of great programs that are not Ivy league schools. Also, if you want to apply to Ivy league schools is it because they fit your goals or because they are Ivy league schools?
I've seen some people go to Ivy league schools (for undergrad) because they wanted to say they went to an Ivy league school, but they were miserable because the fit was terrible.