Do you already have an agent? If so, he/she should be very well qualified to answer these questions and guide you along the way. If you don't have an agent or if that agent isn't counseling you properly and is simply opening the lockbox and leaving you to figure everything else out on your own, then it might be time to consider using an agent who will guide you and advise you properly. You deserve that level of care and should expect it (by the way, if you are indeed looking for an agent, Fairfield is in my market area and I'd be happy to assist you -- feel free to contact me via my Trulia profile or my web site -- see below).
More importantly than the refrigerator should be the location. A home right on the train tracks may be more affordable for you than other nearby homes, but you should also consider the impact that such a location will have on your ability to sell that same home later on. Realize that it could take much longer and require a very aggressive pricing strategy to sell it some years from now.
Most importantly, if you buy a home with certain inherent shortcomings (i.e. location or condition) you should make sure that the price you're paying has those shortcomings factored into it. In other words, if you buy at a big discount today because of the proximity to the train tracks, then you can afford to offer a large discount five or 10 years from now when you sell. But you certainly don't want to pay a premium today and then have to discount the price substantially five years from now over something you overlooked when you purchased it.
Finally, with regard to the refrigerator, everything is negotiable. A refrigerator is personal property and is usually not included, but some sellers will include it in order to facilitate a sale even if they intended to take it with them. In other words, unless the MLS listing remarks show that it's included, if you don't ask, the seller's probably not going to volunteer it.
Good luck...and if you're still looking for an agent, please contact me. I'd be happy to assist you!