Can a 2-way set associative mapping have just one set?
Set index will be 0 or no set index.
Set associative mapping has set identification algorithm the same as direct  mapping which is j mod m, where j is the main memory line and m is the total set count. Here in this case, main memory has 4 main memory lines ( 0, 1, 2 and 3 with each having 4 bytes). Now set count is 1, hence 0 mod 1, 2 mod 1, 3 mod 1 and 4 mod 1 are all 0 which means all blocks will get mapped to Set 0 and within the set 0, the mapping is fully associative. The behaviour and mapping is more like fully associative mapping. hence for a set-associative mapping, a 2-way set associative mapping with 2 cache lines or a 4-way set associative mapping with 4 cache lines etc., behaves like fully associative and set index width is 0. 
Generalizing, a K-way set associative mapping with K cache lines only will behave like a fully associative mapping.