You can theoretically have a higher rate from one lender with lower origination fees and total finance charges may come in lower.  

So if you go that route the $125k down payment will be directed to your mortgage company at closing - not you. 

The two existing LTR units (on my family’s property) were built 5–8 years ago at a cost of about $80,000 per unit, so I’m estimating a 20% increase in costs for the new builds.My plan is to use the equity in the land as the down payment for the construction loan, which I expect will make closing costs the primary upfront expense.

Radiant heat is what you feel when you sit too close to a campfire.

Id keep looking if it was not an approved short sale ( even an approved short sale takes a very very long time and theres no guarantee that you will even close on the house after months of waiting). q1)There are plenty of non traditional lenders that could offer you construction financing if the numbers make sense but it will cost you with points and a higher rate.

My experience is the min is around 15%, but I've read some posts on BP that some lenders can offer a lower minimum (but that usually means a higher interest rate).

Tenants in many markets already believe they pay too much (contrary to recent studies that show rent to property values have never been lower for the large US cities).If my insurance costs are not double my current rates over the next couple years, I will be pleasantly surprised.  

So your $10k could get you a property but what you don't think about is the tenant class is lower and the ups and downs are more frequent.  

A smaller mortgage means lower overhead, which is crucial if you’re worried about vacancies.

If you want to change the design, then do upon closing.