Despite multiple studies in the USA and Europe, there have been no reports of HIV transmission through everyday domestic contact.
Sharing a razor presents a small theoretical risk of transmitting HIV, but sharing razors is never advisable due to the possibility of transmitting bacterial and viral infections including Hepatitis B or C.
There is no evidence that sharing kitchen items such as cutlery poses any risk. HIV is not transmitted in saliva.
Regarding cuts and blood spills, an HIV positive person with an open wound should not be attended to by someone with an open wound themselves. Wounds can be washed with soap and warm water. Antiseptic is useful for preventing all sorts of infections but is not necessarily required. Spilt blood can be cleaned with hot water and normal household cleaning products.