#3 has an easy answer, ask the seller to cover your closing costs (simply write it into the offer).
PMI is for buyers purchasing with less than 20% down. Speak to your mortgage professional to see what loans you qualify for - there are many, many options.
Closing cost assistance can come from the Seller. Ask
I can post the answers to your Q's here but it will take a bit to type out.
Any chance you want to simply give us a call?
617-848-5407 extension 704
Might be easier to go over your options via phone since chances are you will have more questions once I answer the above one's.
And by the way there are plenty of options on the market under $250K
Here is a link that shows you all your opp's in Cambridge:
And all your opp's in Somerville:
Looks like there are even opportunities to buy a Single Family in your price range!
Plus you will see our guaranteed discounts off each property (extra money in your pocket ... which seems might be a huge advantage for you).