That's a really good question. I think laws about what the property seller can reveal to a buyer vary according to country so it's best if you Google it for a specific country. For example, there are laws in some countries about whether the seller must reveal if a death took place on the property (violent [suicide/murder] or natural). In other countries not. I suggest Googling your country's laws on that.
Suicide in a hotel: the police will be called to remove the body etc and that makes the area a crime scene for as long as the investigation lasts, which should only be a couple of hours or so. The police need to determine if it really was a suicide or someone was murdered and the murderer framed the scene to look like suicide. I imagine the hotel will try to minimise the visibility of police in that hotel room and generally on that floor in order not to alarm guests, as suicides do freak people out.
There are some hotels that have a constant string of deaths and people still stay at the hotel (there is one in LA that's famous for murder and suicides, but it's still open which means business isn't affected by its reputation), so it shouldn't hurt the hotel. It's often not reported in local papers that a suicide occurred in the hotel, it's usually through word of mouth (hotel staff or other guests gossiping, which does happen and you can't control). It would be reported in a newspaper if it were a murder, as any murder would be reported.