MacOS – Does the MacBook have malware? Frozen screen and Automatic Clock Reset on Macbook Pro

I like to download books and games on the internet and so my MacBook Pro had acquired some malware. I did not know this, but eventually I installed Avast. It detected that I had acquired a couple of adware and I deleted them. Recently, I performed a full system scan and found 13 infected files. The names of the adware/malware I found were (found some of them in several places):

• Mac-OS-Genieo-V [Adw]
• Win32:PUP-gen [PUP]
• Win32:Malware-gen
• MacO…K[PUP]
• … and several others I can't recall.

I do not know if they have been eradicated, for I did not follow any steps to ensure they are wiped clear from the hard drive—unsure if it was necessary. But then, yesterday, my notebook froze, while I was on Safari. I had not left many programs running, but my physical memory was around 3.99 GB of 4 GB, like it is right now. I was looking up about viruses and adware and clicked on a link, when my screen froze. The mouse neither the keyboard responded. I have recently purchased this computer, last year, and it is not even a year old. So I tried pressing escape (Windows) and a bunch of random keys but it did not work. When I closed it, even then the display lingered on. Finally I gave up and left it till its battery drained away. After a few hours, when I plugged in the charger, it started up normally.

But then, today morning, when I opened Safari, it claimed that Google's certificate was not yet valid. Previosly,this had happened a couple of times. Then I checked the certificate to see that it was validated by April 5th 2015. I then checked the date and time and saw that it had reset to 1st January 2012. Does this mean that my computer is infected? And if so what is the solution?

Here are the specs of my notebook:
Macbook Pro 13-inch, Mid 2012 (non-retina)
OS X 10.9.5 (13F34)
2.5 Ghz Intel Core i5, 4 GB 1600 Mhz DDR3, Intel HD Graphics 4000 1024 MB