You have a lot of research to do. Your questions have been addressed many times here on APC, find those threads for more details.
In summary...
You do not need an aviation degree, any accredited 4-year degree is fine.
However: Ideally you want to major in something very practical (accounting, computer science, engineering, etc) so that when you need a non-aviation job due to medical, furlough, or airline bankruptcy you have some useful training. Some folks will say "major in something that interests you, it's all about self-fulfillment". But in the case of a pilot, aviation is your fulfillment/indulgence...you need a practical major that will be there for you when reality hits you between the eyes.
The school's link was blocked by the forum filters...what is the name and location of the school?