Some will care of nature of incident, others will be indifferent.We've gotten into a property that had a suicide by hanging in the garage and the next buyer felt it had nothing to do with them and didn't blink.Plan extra padding in your budget for worse case scenarios.

There is some risk and, yes, your mortgage will go up, but it you purchase a good, cash flowing rental, it will more than make up for the extra payment

I started a remodeling LLC which has grossed/netted 15k/10k since June working random nights and weekends but they won't count that until it's been established for 2 years (although that extra cash helps). 

Once they lose a case due to procedure, they become bitter and remorseful for not spending the extra money to have it done professionally. 

This can lead to discounts and extra perks as they will witness your commitment in building relationships within the real estate community. 

also what 30 yr fixed  rate are you considering and what are the closing costs/ loan fees  associated  with the refinance …..you might ask  for  " low cost "  rate options for the refinance  in order to keep these expenses down …...if you refinance the loan to a new  30 yr fixed in order to make it cash flow better - always keep in mind that you can  apply extra payments to the new loan to  whittle the balance down

Boroughs, Long Island, Upstate, Westchester, over the bridge in New Jersey, literally anywhere.I will do whatever it takes to earn the money to buy property to live in.

"Off market" and "For Sale by Owner" properties come with no such guarantee, so buyers agents will not be knocking down your door to earn one side of the commission for doing the work of both agents. 

I’d say maybe they want the extra room as a luxury like an in home office.

However, if they wanted to justify it, I'm sure the justification is that renters cause more problems than owners; renters tend to live then shorter periods of time and there are expenses when someone moves in/out such as extra trash pick-ups, programming them into an entry system, cleaning costs as the move in/out can be messy around the building, light damage to the building, scheduling of the freight elevator, cost of providing additional notices as now the tenant and owner need to receive copies, etc.