We collect first, last, and a security deposit equal to one month's rent when we turn over the keys.

Generally the seller and buyer sign a form acknowledging the procedure and agreeing any difference between what was collected and what is owed will be settled between then and is not the responsibility of the settlement agent.

I assume there’s a government department in charge of collecting these fees, why else would they require licensing.

If they do, that is an early sign that that person may not be the right tenant to occupy your property.Collect DepositsThe standard security deposit is usually equal to one month’s rent, but some states law allows property owners to collect up to two months’ rent for a security deposit.

They all offer rent collections, work order management, portals etc....how they do it is different. 

Do you know where I could find rental collection data? 

If you read beyond the highlighted portion, HUD provides "best practices" for what information the Landlord should collect.

What program, app, or website do you use to collect rent?

I am worried that I am paying too much for turnover/major repairs without collecting multiple quotes...

There is a grain of truth in that impression, but it's a case of confusing correlation for causation.