@Joe Garvin - what exactly are you looking for? Any specific advice?
Just by going over the numbers quickly, I have a few questions / comments.
First question: You say that rent should be raised to $900, seller says $850. If it could be raised to $850, why didn't he do it? Sellers usually raise rents as much as they can in order to make their property look like a better investment. Where did you get the $900 from?
Advice: Check out RentJungle or RentOMeter to compare local rent rates. This can give you a good idea of how much an apartment will go for based on size and number of rooms.
First Comment: Good job running another look at the numbers. The seller states a cash flow of almost $500 per month, but this never takes into account maintenance, CapEx savings, vacancy, etc.
Second piece of advice: You only have 3% CapEx savings per month. The property has already had work done, but it isn't a new construction. I strongly suggest raising CapEx to a minimum of 5% per month, with an even stronger recommendation of putting it closer to 10% per month. Older buildings are more prone to needing larger-ticket items, and it will always feel better to pay out of a savings account rather than out of what you had originally thought was profit.
Suggestion: You know what your expenses will be (8% maintenance is fair, raise CapEx to 10%, vacancy of 4% may be low, insurance I would get a quote on as your rate seems high). Don't play with expenses, thinking that you can cut corners to increase cash flow. Your options are to increase rent (RentJungle will tell you how high you can expect), or decrease your financing payments (decrease purchase price, negotiate for a lower interest rate, etc).
My philosophy: (Almost) Every investment property has a price at which it would be worth it for me. If I know my expenses and income, I can find a purchase price that will bring my mortgage down far enough to provide my target cash flow. There are always exceptions to this rule, but they are usually extreme.
Advice: Decide what you want. If you are looking for a cash flow number (say, $200 per door per month), you can find a purchase price that will give this to you. That way, you know what your bottom line is and you won't slip past it while chasing a property.
If you are looking for something more targeted in feedback, ask away!