NOTE: if you have rentals in California, be sure to buy the California edition because it is the most regulated state and requires a separate book.

Two completely separate things.

House has been on the market for quite sometime, originally at 349,000 now 299,000. old historical mansion, 3 bedrooms, keep up fairly well, with a separate entrance 3 rd for 1 bedroom apartment. 

I recently learned that even collecting first and last follows similar guidelines where we should be opening a separate account to allow for interest etc.  

It sometimes easier to keep your funds under one bank, but in separate accounts.

Well a bank isn't going to lend to a LLC with no history or assets, and since the IRS doesn't consider a LLC a separate entity the bank might not either. 

2) Will I need a separate program for background checks and what should they cost? 

The best way to do it is in a separate bank account LLC or not.  

In the fourplex I lived in, the owner was extra awesome and provided poop bags and a small separate waster container.

If the units aren't separately metered and there isn't a RUBS in place, then you definitely need multiple years of expenses to make an informed decision.There is really a lot to learn about multifamily, and I would say it's more important to build a strong team than it is to learn every detail.