Malwarebytes having found nothing doesn't mean nothing is there, the problems you're having seems to indicate something is!.. particularly an Adware that may not be detected as particularly malicious but they are still undesireable.
No antivirus or antimalware is a 100% effective... years back the notion that security applications were only arond 80% effective because of reasons like they not having deffinitions up to date on the latest released bugs.. other reasons could be due to malware attacking the very same security programs, and maybe corrupting their deffinitions, this would probably be the simplest way of programming malware to avoid detection.
The yugoslavian website on the DNS error seems like a distinct possibility, If you check the Internet Options > Privacy on cookies you will see that third party cookies are an obvious possibility... this party cookies are from websites you never accessed. So that seems to be what your DNS error indicates. Possible solution can be a "custom Hosts file" you can download one from different websites, just type that on your browser for details and downloads.
The Msmpeng: is part of MSE, and so is Alexa, which was (or is) also detected as adware.. so them being genuine MS doesn't mean they are desireable or perfectly safe or even invulnerable to infection and takeover. Besides Microsoft has been accused of including spyware in the Windows Updates.
Steam and games: I have always considered Gaming websites to be a viable route of infection. In the past I noticed that games websites were one of the riskier type of websites... children computers are usually infected because of their browsing habbits, and from children to adult games there isn't much difference.
No I don't have similar website issues... whenever such a problem appears I can usually recognize their activity and solve such issues. In my case it's happened whenever I got careless when installing applications as they usually install extra applications if you don't carefully watch the installation process. You have to always select the Custom installation as opposed to the default installation so you can uncheck undesireable adware or malicious software installation.
On Tom's Hardware: I believe the main purpose of adware is to record the user browsing habbits and send relative data home... so my guess is, whatever adware is in your computer, it reacted to Toms Webiste possibly due to the type of assistance the forum provides, and this reaction may be what the Event log recorded.
I don't know much about Nvidia issues or their relation to steam or memory leaks, but it sounds obvious to me that any of the Power Options, Hibenation, Sleep Mode or simple standby must have an influence on video (specially noticeable when you can't awake the computer from sleep mode), so Nvidia drivers and the driver manager issues may be traced to Power Options, and the steam.exe crash may be a consequence of this. If you consider that any of the Power Options saves data to the RAM modules, and this in turn can have influence on video and video drivers, you can conclude that there may be some relation between your absense, sleep mode, and the whole problem... not considering a coincidence with adware issues.
I would suggest you delete temp files and system junk, disable startup programs, disable System Restore, clean the registry, etc. and then do more virus and malware scans.. including a HijackThis scan. Check the thread on usefull tips in cleaning any computer from residual files, bugware and more, to improve security and performance.
http://www.tomshardware.com/answers/id-1863469/slow.html