When Pearl plays around changing Mike's name in the contacts on her mobile, it's eventually saved under "D". But when she seconds later receives a notification about Heidi's alarm system, his name shows as "Mike" and is stored under "M".
There appears to be minimal time lapse between the murder and the funeral of the victim. It would be highly unusual in the UK for a funeral to take place within a day or two of the death (other than Jewish or Muslim funerals, and in this case a Christian priest is involved) and especially so in the event of murder.
There is no significant indication of any investigation going on during the intervening time.
When Mike arrests the perpetrator, he says "You are under arrest for the murder of Brian Armstrong and the attempted murder of Paul Armstrong". But Clive is the correct, as there is no Paul.