My question is were there some diseases which had occurred among people living in the Americas, which they were asymptomatic carriers of? How come Native Americans didn’t pass any diseases to Europeans? Did European lack of hygiene play a role?
The disease load of the Americas before 1492 included both pathogens that made the trip to the New World with the original migrants as well as infectious organisms that made the jump to humans after they arrived in the Americas. Humans brought intestinal parasites (hookworm, roundworm, whipworm, pinworm, etc.) and tuberculosis with them from Asia. New pathogens, like syphilis and Chagas, either jumped to humans during their stay in the New World or evolved from existing pathogens into a new, more pathogenic form once in the New World.
Analysis of coprolites (preserved feces) and mummified remains allows us to acknowledge the presence of those previously mentioned intestinal parasites, Giardia, Entamoeba, and Cryptosporidium (among others) throughout the Americas (Goncalves et al 2003).
Sometimes epidemics strike quickly and fade away. Pathogens and their hosts are constantly evolving and humans are constantly subject to new infections. Zoonotic infections (pathogens that jump from non-human animals to humans) make up the bulk of modern emerging infectious diseases (Jones et al. 2008). Populations in the New and Old World could easily have seen brief flare-ups of zoonotic diseases that died out as quickly as they started (think modern instances of Ebola outbreaks). We would likely never see evidence of these flare-ups in the archaeological record, but if modern populations exposed to wildlife and the bushmeat trade are subject to zoonotic infections there is no reason to think past populations were immune.
Finally, small changes can lead to epidemics. Sometimes a previously benign, or contained, pathogen can flare up into an epidemic. We don't know the prevalence of cocoliztli before contact, but shortly after contact the disease burned through Mexico. Cocoliztli is a Hanta Virus-like hemorrhagic fever that swept through Mexico in the sixteenth century. Two cocoliztli epidemics, in 1545 and 1576, killed between 7 and 17 million people in highland Mexico. Researchers believe the pathogen responsible for the epidemic did not arrive from the Old World, but rather widespread drought caused conditions to change, and a home-grown New World pathogen became a terrible epidemic.
So, we know there were quite a few pathogens circulating in the Americas. We know of a home-grown infection that sprung up after contact, and there is good reason to suspect an occasional zoonotic disease epidemic perhaps caused a brief increase in mortality.
Now, to the idea that Native Americans didn't pass disease on to Europeans. Europeans often fell ill in the New World, and in many cases we assume these deaths were from diseases they encountered in the Americas. When we read the accounts of early Spanish entradas in the U.S. Southeast, the authors make specific mention of crew members becoming ill weeks after their arrival in new lands. Nutritional and physiological stress from poorly planned colonization attempts likely decreased their immune defense, leaving them vulnerable to illness. Ayllón's 1526 attempt to establish a settlement on the Santee River in South Carolina ended in disaster. Of the original 600 colonists, all but 150 died from hunger and disease. Later, the 1528 Narváez entrada likewise suffered a series of unfortunate events in their attempts to find riches in Florida. 400 men landed in Tampa Bay, yet only four survived the trip to Florida. After a month of raiding Apalachee towns, members of the entrada began to fall ill. Cabeza de Vaca says
there were not horses enough to carry the sick, who went on increasing in numbers day by day... the people were unable to move forward, the greater part being ill.
Did members of Ayllón and Narváez's entrada perish from New World pathogens, or did they bring their own microbes with them, and perish as a result? We don't know for sure. The deaths began outside the incubation period for many common pathogens, giving us reason to suspect they did not bring those illnesses with them from Cuba, but rather encountered them from the neighboring maize-based agricultural populations like the Apalachee. Similar European mortality events are noted in Jamestown, where of the > 3,500 who arrived from 1617-1622, only 1,240 were alive in 1622. The chief cause of death was endemic illness, and the term "seasoning" was commonly used to describe the disease transition new immigrants needed to go through before their survival was more assured. We don't know for sure if the seasoning illnesses were infections brought from Europe, or if they included pathogens encountered for the first time in the New World.
To sum up, the popular assumption that Europeans did not encounter any new pathogens in the New World looks to be wrong. As we dive into the primary sources we find abundant evidence of infections, but it will always be a little difficult to determine, with 100% certainty, that those illnesses were from New World pathogens alone.