I would get your criteria including ARV for different neighborhoods & max allowable offer down with precision, then set up searches on the major MLS sites, including a search you've set up with a realtor, & get your pre qual letter ready to make an offer the minute something comes on.

Have anyone had experience renting by the room and mix males and females?

Just make sure that you fill out the paperwork and submit it on time and follow the regulations to the letter.

Is it normal for the seller of a multi-family property (5 units) to ask me, an investor inquiring about their property, for a Proof of Funds or Pre-approval letter when I am just asking questions like to see the rent roll, losses and profits for the last 3 years and other relevant info to do my due diligence? 

So today I recieved a letter on my door as well as all my neighbors saying that they are aware of people indulging in illegal smoking substance.

sa=t&source=web&rct=j&url=https://www.michigan.gov/documents/ag/Ltr.M.Landau.4.16.2020_687458_7.pdf&ved=2ahUKEwjNo-TpxpjpAhUPna0KHQjRCSMQFjAAegQIAhAB&usg=AOvVaw2o1lSNwOQHQ-4cT8sUHOv8Not an article, but a cease and desist letter from Michigan's AG forcing a Detroit landlord to allow 80 rent-striking residents to live for free.

There are multiple reports on other websites of banks lowering credit limits or closing accounts altogether with no notice at all, just a letter in the mail. 

In December of 2016 I sent out 500 direct mail letters to duplex owners in SE Portland.

Do I send a single letter to both, a separate letter for each, or three letters: one addressed to both, and one to each of them ?

Make the letter/receipt professional and polite.