My wife and I will be officially taking over ownership of a property management business in September of this year.

In the mid 2010's they made an exception for transferring into your own LLC. 

3) Around how much should we expect in transfer/title fees to get the house from our relative’s name to our LLC (yet to be formed as my brother and I are looking to create a joint one specific to this house)?

This way we're effectively each covering 50% of the cost of his timeOption 3:  the uneven splitWe can figure out another split of ownership that makes sense for both of us to be happy despite the fact that we'll contribute equal capital to our deals.

At no point were the current leases transferred to new owner.

I would not transfer over to selling real estate yet, if at all. 

It depends on how the title will be held.There are two ways that ownership of title can be heldTenants in Common(should have a TIC agreement)Through an entity(LLC, LP, Corp, etc)

Can I simply receive funds from a private money lender transferred directly into our business bank account?

You can buy that way and get a conventional loan but Fannie allows you to transfer it after.

Even today, I see young investors dropping their properties after less than five years of ownership.