2/ Visual reference is not particularly accurate. Some nematodes and trematodes are visible but not always. Microscopy is the most accurate and involves looking at the ova which is the most identifiable part of the parasite. Most labs are not equipped in identifying. Nematodes have distinctive tapered head/tails - Tapeworms have specific identifiers such as white rice which is the ova.
3/ There are other matter which can be mistaken for parasites.
4/ There are many organisms that can inhabit the gut including yeast/fungus, rogue bacteria, viruses and the overlooked parasites which are protozoa.
There is not a specific Science regarding parasitology and imo has so many holes from proper testing to proper treatments. Most doctors have no clue in any of this. Treatment strategies are generally weak.