For question 1, I think you are safe but if you are super concerned, you could rinse the spoon in a chlorox solution before drying. The little residue that would remain would not affect fish or filters. For question 2, Yes. Parasites require a host and without fish there is no host. But, there are parasites on all fish all the time, the numbers are insignificant, and will remain a non-issue unless the fish are stressed by poor water, major temperature changes, or water parameters that are less than ideal, at which time the parasites will multiply to numbers that cause issues with the fish.
Zone 7 A/B
Keep your words sweet. You never know when you may have to eat them.
Richard