The carpet and car interior can be cleaned using hot water extraction and a suitable microbiocide. However depending on how big the underlying dampness problem is you may be wasting your time. The visible fungi is only the fruiting body, the underlying mycelium (roots) are many times the size and will have penetrated the underlay, flooring etc.
Sounds like the property has a major dampness problem. The root causes of this need to be addressed rather than attempt at cleaning.