I also learned the laws, made sure I did everything by the book, and covered all my bases.

If they're month-to-month then you just need to give them 30 days (or whatever your state/local laws require) notice of the rent increase, however seeing as the current owner has not increased rent and you're the "new guy" coming in, don't be surprised if the increases are met with anger/hostility.

Also make sure you’re in compliance with any state laws on how much you can except from tenants in any particular window.

Sounds like you know that you are supposed to have your properties titled in LLC's but law suits are something that happen to other landlords, right?

The cars on the front law could be a liability issue. 

My husband and I are soon to be brand new landlords....My father in law recently passed away and we will be taking ownership of the home.

I am not familiar with the laws in your geographic area and will suggest you familiarize yourself on your city's and state's tenant's rights, specifically landlord obligations of habitability.

Actually on the day I closed I came to know that the city I brought my rental property has a law that I need to have property management firm to manage my property if I live out of state.

Laws on some particular subject matters do tend to differ from state to state, but, their refusal to accept your "Affidavits" seems absurd.

Know the law, obey the law, treat people honestly and fairly.That will protect you far more than any LLC or insurance policy or attorney.