Testing and detox
I would doubt that removing any heavy metal is going to directly remove a parasite, especially the nematode/cestode classes. Although it has been conclusively proved that metal toxicity will weaken the immune response, so a person w/o heavy metals would have an easier time to remove the parasites.
When speaking of lower class pathogens (protozoa, bacteria, viral, fungal etc) there is more substantial information that would suggest that metals play a role in keeping these pathogens in. Fungal infections come to mind as they are "mercury loving".
The only proper test to consider is a Heavy Metal Challenge. Hair Analysis is an EPA recognized test for metals, but the shortcoming of HA is that it is only valid for recent exposures -say for instance you work at a metal processing plant in which you exposed to vapors (metals), then since the exposure is constant the hair will pick this up. For some, the body sequesters heavy metals, putting them into "storage" locations. For instance mercury has an affinity for storage in kidney, heart and neurological, whereas lead has a tendency to accumulate in bones etc.
There is evidence that anti-oxidant status plays a key role in determining if metals will be deposited in storage or expelled from the body thru the liver/intestinal tract or thru urination. Glutathione status probably plays an important role in this decision. N-Acetyl-Cysteine (NAC) is a converted form of cysteine and a precursor to Glutathione production. There are many other nutrient factors (amino acids/mineral/vitamin co-factors) that play a role in production of glutathione. This is also known as methylation.
A Heavy Metal Challenge is a test in which urine is collected after a short-time of an IV infusion of EDTA and DMPS, 2 chelators. EDTA is specific for all metals except mercury, that is why DMPS is used. These chelators "force" heavy metals from their storage sites, thus when the urine is collected an idea can be formed as to true body stores of metals.
Chelation is controversial as to the proper methodology. Some of the pharmaceuticals such as EDTA work by way of covalent charges, meaning that it attaches itself to metals which include both heavy metals and essential minerals. So proper supplementation of beneficial minerals is absolutely key. One of the benefits of this type of chelation is that side-effects from metal removal is lessened.
There are other practical ways to remove. For instance chlorella is a very good "vacuum" of mercury, however it does not directly force the mercury out per se. Oftentimes people will use cilantro in combination with chlorella. A website called naturopath4you.com has extensive protocols including nano sized chlorella, Modiflan etc.
Some homepathic remedies (Dentox) has shown some promise in chelation, I would suggest using chlorella to help lessen the effects. I have heard that some detox clays are effective and IR sauncas as well.
Detox is not a short-term process, oftentimes it can take sometime to remove a significant amount.