New ProRet: Slow when shutting down, mouse freezes

Hello everyone, I'm new here so welcome any suggestions if I'm doing something wrong. This is my first mac, I've always only used Windows.

My notebook is a Mbook Pro Retina 13inch mid-2014 (bought in Nov). Running OS X 10.9.5. Memory is 8GB and storage is 121GB (currently 75GB free), it only has the applications and the odd Word file, for itunes library and pictures we use an external hard drive.

I don't think I've done anything too bad to it, but I did install a couple of applications a few days before the computer started to go funny: Popcorn Time, but deleted it after 2 days. Then it went a little bit slow so I downloaded and installed CCleaner for Mac and ESET Cyber Security, in case Popcorn Time had virus or malware, but nothing came up in the virus check.

Up until last week, it was running okay, very fast turning on and shutting down, no freezing, no spinning beach ball. But last week, the display went distorted for under a minute (gave me time to take the picture I'm attaching) and since then, every time I shut it down, it takes longer than normal and shows a spinning wheel on a white background. Yesterday, the first episode of non-appearing pointer happened but very briefly, only a few seconds. However, today I was busy typing on Microsoft Word and when tried to use the trackpad, the pointer wasn't there, never appeared again, I could no longer even type anything and neither F4 or F3 responded. Tried Command+Option+Esc and nothing. Pressed shut down button for 3 seconds but the pointer didn't respond to click on any of the options, so had to force shut down with the button. Now I'm scared this will happen again and I will have to force shut down more than is safe.

In case it's relevant, we use the HDMI connection a lot to watch movies on a TV and the display does sometimes move around or briefly show horizontal line but I assume it's normal when plugging in a hdmi cable.

Does anyone have any idea why this could be happening and is there a way to find out what is wrong with it? I wasn't expecting to have problems so early on with a macbook :/

Any ideas will be most welcome (I've no idea about changing system settings or the like).

Thank you