dampness

I aked this question on reddit but it was suggested I sign up to this forum as there are far more experts on here so here goes! I've been asked to paint the outside of an elderly relative's summer house .It looks to me like it's never been painted and appears to have some kind of dampness or...

We've recently found patches of mould on the living room wall. One patch low down in particular (in photo). But mostly isolated spots across just the one section of wall (the one with the outside wall). There's also some marks around the mains socket, which doesn't look like mould, but possibly...