The response to the pandemic requires access to accurate information and public understanding and adherence to preventive measures. This online cross-sectional study of adult Poles (n = 1337) assessed the frequency of COVID-19 preventive behaviors, fears related to the COVID-19 pandemic, and beliefs in COVID-19-related conspiracy theories during the early phase of the COVID-19 pandemic when the nationwide lockdown was imposed (April 2020). As shown, 22% of surveyed admitted not to wash their hands frequently, while 12% did not use disinfectants. These two behaviors were also less frequent in individuals with medical education. The highest levels of pandemic-related fears were associated with health loss in relatives, pandemic-induced economic crisis, and government using a pandemic to control citizens by the state. A significant share of surveyed individuals believed that the pandemic was intentional action to weaken non-Chinese economies (32%) or was deliberately induced for profits from selling vaccines (27%). Men, individuals with no children, and subjects with lower education were significantly less likely to adhere to sanitary measures (handwashing, disinfection, avoiding face touching, changes in greeting etiquette, face-covering when coughing or sneezing), and were less concerned over self and relatives’ health. At the same time, men were less prone than women to the conspiracy theories related to the COVID-19 pandemic. The results indicate that adherence to sanitary measures during the pandemic can be a challenge also in developed countries, while misinformation campaigns (also concerning vaccines) have already affected the general public during the early phase of the epidemiological outbreak. The study provides observations that may be useful in the management of the public response to future epidemics.