How old is the roof? Doesn't look like it was built in 1955.
As young as this roofing is in years, someone must still have valued the house at this investment. Let us assume it was not a madman, and derive a suspicion from that that a hopeful look at the entire substance is still worthwhile.
The neighbor was already there and said that in case of demolition he would take the roof tiles.
A usual demolition turns everything into rubble. For reusability, a roofer must come here, so dismantling (probably best also with scaffolding) instead of demolition.
I would definitely heat the basement. A basement is far too valuable to misuse it just as storage space. And therefore, I would not waste any consideration on preserving this damp basement.
I consider it worth checking whether the basement is objectively as shabby as it appears superficially; and in that case, I would dedicate it only to utilitarian purposes.