1. That what savings are for. Besides an emergency fund, savings are actually losing money sitting in the bank. You should probably go get another $100K before investing.
2. I would recommend a market that you know very well. The numbers in Memphis are off the charts, but it's a rough town and you need to know how local people feel about the area you are buying. Find a neighborhood or zip code, learn it well, then buy. Property management and repairs will be the biggest challenge with being out of state, which is why I don't do it. Nobody will look after your stuff as well as you. You should consider moving. Whatever you do in NYC for work, is also done in other states.
3. You may find one listed online, perhaps on FB marketplace or wholesalers. You will likely need to market to landlords who want to retire. Running ads on FB, craigslist, etc. Property managers can point you to these landlords. Also, probate attorneys.