1) Possible, but doubt it. Router has been changed no less than a year ago, tops. But it's Belgium, who knows. Moving to sweden in a few months, though.
2) Not completely sure what you mean by this. If you mean the wall socket, then it shouldn't be the issue at all.
3) Driver could be wrong, but I've only been experiencing this issue since this year, for since I've had the computer. I don't recall changing the driver (Checking it, the network adapter driver was last updated 2014. Maybe that needs an update then? It says it's up to date, though, when I ask it to look for updates. (I restarted my PC so I have a DNS connection now for.. a day or so anyway.)
4) Definitely no malware on it.
DNS works in safe mode, until of course I lose connection to it again somewhere along the way. Can go for a few hours to a few days.