So let's say that the inquisitor is next to a royal guard when he gets attacked and he rolls a blank on his white die. Would he get two blocks (1 for defensive and 1 for protector) or just 1?

Along the same lines, could a jet trooper convert the block that the guard gives to a surge protect?

One block from Defensive for not rolling a block, and one block from Sentinel/Protector.

Because both abilities are defender abilities with the same timing (both add or remove symbols), you can first resolve Sentinel/Protector which adds a block to the defense results, then Agile to convert a block in the defense results into an evade.