Yes. You can restrict the number of people who can live in a unit, but the best practice (also the recommendation of the Fair Housing Council of Oregon) is that landlords follow a “two plus one” occupancy standard. This means that there would be two people allowed per bedroom plus one extra person. Many landlords hope to be more restrictive than that, but being more restrictive than the 2x bedrooms +1 formula greatly increases your risk and liability. This is why our company subscribes to the “two plus one” standard.
Your property can absolutely be advertised as having a no pet policy. The important distinction to draw is that a “service/therapy/assistance/companion animal” is not a pet. The terms “assistance”, “companion”, “therapy”, and “service” animals are all interchangeable in terms of the Fair Housing Act (FHA) and under the FHA, residents only need a note from any health care provider that the animal is necessary to accommodate their disability. No certification, registration, or training of the animal is required. Here is a link where HUD outlines reasonable accommodations under the FHA.
It is important not to confuse this with the standards for animals in public spaces. Public spaces, not covered by the FHA, are covered by the Americans with Disabilities Act, which requires that animals in public spaces (transit, restaurants, libraries, etc.) be a “service animal” that must be registered and trained. This is a much higher standard than housing.