In the gas trade I last counted something like 60 documents to comply with...I think that says it all. So many contradictions and gaping holes.
Unless it is a particulary exposed site the lack of seal does not normally cause an issue, that is why the manufacturer does not insist on it.
The bricks are old and the one near the flue has clearly spalled, once the surface has gone they rapidly deteriorate...the rest of the pics look normal wear and tear.
Get the holes sealed, get the humidity under control. Is there a bathroom extractor OVER the bath (not stuck in a corner short cycling the sir), is there kitchen hob/cooker extractor to outside, is there background ventilation (there appears to be nothing over the windows). Then go from there...