Problem 1: Hint

This problem is made much easier with a little more information.

Splitting of a signal into a doublet, triplet, quartet, etc is due to spin-spin coupling between nuclei with non-zero nuclear spins (I). Hydrogen has I=1/2. We know that hydrogen will split the carbon signals if the carbon spectrum is not decoupled from the hydrogen spin. For problem one, the carbon spectrum is decoupled and still we see splitting! That means that whatever element is splitting the carbons must have I=1/2 just like a proton! Find the element (halogen) that has I=1/2 and the problem will become much easier.