Most of the educational materials I have seen on running the numbers just talk about a percentage per month for property to do a deal analysis.I know that could be the case if you are just looking for tenant placement and you are going to self manage thereafter. 

One complicating factor is that we all plan to contribute different percentages of the down payment; we are thinking through how to account for that in the agreement (for example, the person contributing the least upfront may take on a greater share of the mortgage payments for a period of time, etc.). 

The best REI never stop learning.As far as your questions (at least the vague ones you state here) are concerned, the only way to get answers from the people you asked is with a specific property...with complete numbers (with dollar signs in front...NOT percentage signs behind).There are way too many specific strategies that I have been associated with through action and teaching to mention here, but you're not ready yet to execute any of them yet...so it really doesn't matter. 

Here are your problems:1 -   You're spending so much time trying to figure out if a Section 8 situation is a possible solution to get her into the property financially, that you've caused an even bigger problem.2 - You're ignoring the math3 - You're analysis is based on theory, conjecture, and (this should never be used here) percentages.4 - You're timeline is your enemy, and you're not factoring it into your analysis.5 - You're success is based on future events that you have no control over.This property/solution is a financial disaster waiting to happen.  

On a 16-unit you'll realize some efficiencies of scale, so could knock that down a couple of percentage points.

It sounds like the percentage they are charging is a regular markup... after all, they sourced the vendors (likely have already worked with them for years, in fact, and so the vendor is more trustworthy and fair with them), coordinated the repair between vendor and property/tenant, and took care of the payments. 

But can the down payments be a smaller percentage?

What percentage of the year are you doing STR versus LTR?

Prices have gotten unrealistic for real estate, so I am prepared for a price correction, or for a long-lasting crisis, depending on the country.çIn Europe the only way to maintain the welfare state is charging more taxes and one of the easiest way for governments to get more money through taxes is focusing on real estate (property tax, a tax percentage on properties that are vacant etc)

In reality rather than a percentage it should be a dollar amount.