In smaller communities, it's not uncommon for the local government to enforce their own interpretations or rules placed at the state and local level.
In short, evictions are happening, even if they shouldn't be in many cases. And as moratoriums expire in the near future, we should expect many more Americans to become homeless or evicted due to the failure of primarily the federal government but some local and state governments as well.
Washington State, as an example, has publicly spoken out about unlawful evictions and has warned to pursue legal action against property owners that violate the state's moratorium on evictions. For example, just one example from April 2020:
https://www.q13fox.com/news/washington-attorney-general-dire...
Washington State's moratorium is currently set to expire in December:
https://www.kiro7.com/news/local/states-eviction-moratorium-...
No, they are not. Not even close to almost everywhere.
Evictions are theoretically suspended in many places, but rent is definitely not and many suspect land / property owners are evicting people despite moratoriums on them due to local governments that are severely underfunded, understaffed, and/or overwhelmed that are not enforcing the moratoriums.
Ultimately, this situation can almost entirely be laid at the feet of the anemic and mismanaged response by the federal government. Most of this could likely have been prevented if stricter measures had been taken immediately. And even if they hadn't, most people could be far better off if it wasn't for the extreme levels of obstructionism and denial being exhibited by parts of their federal government.
Financial assistance should have been sent directly to individuals across the country instead of being absorbed by corporations that just wanted free money.