I'm getting too old to tackle anymore major renovations. The house I bought a year ago was built in the 70's, and I just changed 3 windows out myself. I was installing some trim today. You would not believe the price of pine trim. I needed some square flat trim. It was very small stuff about 3/8x"1"x 6ft pce $16 can ea before tax. Even if your labor is "free", the materials cost a whac these days.Yes they most likely use the wood and oil at the same time. My grandpa had a setup like that on a 8" clay lined chimney. Oil in the basement, woodstove on the first floor.
You are certainly entitled to your opinions, but it looks like a nice place to me and not a lot to fix up really. Definitely not a tear-down. But that's just based on some photos