If the seller is encouraging you to NOT have professional representation that protects your best interests, that is a major red flag. Imagine if someone sued you then said hey, let's all save some money and leave out the attorneys! Would you play ball, or say "no thanks, I'd rather have my attorney represent me."
It sounds like you're a sweet, good-intentioned person who takes the "mutual friend" thing to heart. I can certainly understand. But when it comes to investing in a piece of property with your hard-earned dollars, you really need all the protection you can get. If I were you I'd tell them that you need some professional representation because you've never been in this situation before and you don't expect to gain an education in this over night (and like Michael said, a potentially costly one!). Tell them that you're flummoxed, that you're apprehensive, and that you don't feel comfortable moving forward without a real estate professional by your side. If they have the slightest shred of empathy that you clearly have for them, they will see your point, give in, and you can have your representation. If not, they simply care about their own interests and you have exposed their true motivations. Either way they react, you've discovered a lot, no?
It also sounds like value is your main concern, particularly since the home needs work. As an ex-appraiser, my clients find my expertise in this department invaluable. You are absolutely correct that valuation is a big challenge in this rapidly-changing marketplace. Sellers are chasing a moving target. Price is everything right now. I just wrote and article on my blog about how current conditions benefit buyers such as yourself - you may want to check it out here:
If you need advice and someone that will get into a very detailed analysis on whether or not purchasing this home is a good idea, please call or email me and we can discuss. My final thought is this: have representation no matter who it is! I wouldn't proceed without it. Wishing you all the best...