Hi Fiona and welcome to Real Estate Investing 101! You could not have come to a better place.
I currently live and invest in South Carolina but I can give you my ideas and I'm sure others will comment.
First, I'm assuming you are investing 3 hours from New York City due to prices and competition. I cannot comment of the validity of that but I will tell you that once I am comfortable with my local knowledge I will be investing in Indianapolis (wife's family area) and will find myself in the same boat as you.
So, to question #1 - Vetting numbers is the same everywhere. Set your parameters and do not stray for ANY reason. The MLS is a fine place to start. When I first started looking at properties here, an agent, who I met quite by accident, showed me two properties she said would work for investments. I had paralysis by analysis back then and passed on both. Both were eventually flipped and provided fairly handsome profits. I discovered this after I became an agent and had access to the MLS myself! So do not discount the MLS but in addition, use this site and any local REIA's to find wholesalers and agents in your chosen area. Believe me they will come out of the woodwork if they know you are in town and have money to spend. BUT, and I can't say this enough....know your limits and stick to them.
#2 - I am a retired contractor myself, but this is a different game. Where granite is the low end of most custom homes these days, formica and chrome will become your friends! Not that you need to actually do the work, but certainly understanding the process and what to look for in a contractor or partnering with someone who does, is of huge importance. A great book that will help you learn what/who to look for is J Scott's "Book on Estimating Rehab Costs". What you learn in there will help you vet the contractors and make sure you are getting the most bang for your buck. Oh, and set your keywords here and keep asking here. Someone will know someone!
#3 - Have not done that yet. Will let you know when the time comes!
#4 - Finding an agent is tricky. I became one for access to the MLS, but have sold several conventional deals through open houses for other agents in my brokerage. That has exposed me to good agents and agents who are not interested in the least in investors. Make sure the agent IS an investor or works for some in that area. Then hand them your criteria and see what they bring you. Most will not want to run 200 deals or write 100 offers to get you one, but the conversation will lead to what and who they know, along with what they are willing to do in your absence....hold open houses, help stage the homes, put you in contact with like minded buyers, even keep an eye on the project in your absence, etc. If I thought I would make 3k or 4k for the effort of driving by a home I was going to get the listing on, to let you know whats going on, I'd do it in a second!!
#5 - I do not have property worthy of paying a property management company yet, but rest assured, I will use one when that time comes! And it will be in the area I LIVE IN! I want nothing to do with leaky faucets while Mickelson is on the 18th hole at the US Open on Fathers Day with a chance to finally win! Figure the 10% into your numbers and pay it. You will sleep much more soundly.
That is my two cents. Disclaimer; I am a rookie as well. My only experience is that I know the construction game and have made some good money from flips in easy times....this is a different time but there are a million articles in here about reacting to different markets so I plow ahead...sort of fearless at this point!
Best of luck to you Fiona! See you on the forums!!