you have a various set of operations with both methods - poly and nurbs. thing is, to break it down simply - you have to have some experience and understandig to work with them in maya. I may be mistaken but it sounds you dont have much experience with maya.

anyway. what i can tell fast is (coz i work a lot with architecture and maya) you can make boolean operations. stick together 2 shapes and make 3 possible new forms -> minus A from B, A+B, and intersection volume. you can project curves onto surfaces and create from those projections new curves on surface and so on...

ad1) yes and yes. maya got mirror cut tool which works like this. you could also do it the other way.

ad2) create curve from plane edge (90°) and goto orthogonal view then do a "cut curve" operation. there are many ways to do something but it did cost me quite some time to get pieces together.

good luck!