I find myself in an odd position.

The odds of hitting an owner at the exact time they are motivated enough to sell with a direct mailing piece are very low.

Everyone and their uncle is out there marketing to motivated sellers and some are spending small fortunes every month on marketing - You just can't compete with that - Thats not to say that you won't eventually stumble on a deal, but the odds are against you.  

That's odd.

a 1/1 being call an apartment seems odd, but it might be part of a mixed use building.

From the city's perspective they have reasons for their restrictions and permits.

Interest rates are extremely low right now and you have very few restrictions of how you can use the money and it is simple to do.

Even doing 30+ day rentals, you are exempt from the sh0rt-term rental restrictions, if that's what exists.

Banks give preference to owner occupants and often insist on holding period restrictions.

Zoning and other restrictions are really loose here.