Why am I constantly getting "Google Play Services" error messages? Note 3

It happens whenever I'm in a game or application, (occasionally when I unlock my phone) but following the error message my game or app never crashes or freezes; nothing happens. Also, one time it said "Samsung keyboard has stopped" and my keyboard froze for a minute or two. That scared me. Also recently some, not all, of my applications have been freezing and then the "This application is not responding, do you want to close it" error message pops up, but never after the Google play error message. Could that still be related, though? Coincidentally, (or not) this started happening after I found the cause, (a virus that apparently downloaded itself) of full screen pop ups and ads and was able to uninstall it, no more ads but now I'm having this issue. It's not to the point where it's interfering much, but looking up other's posts similar to this, I've seen people saying they get the Google Play Services error message up to 10 times a minute, making their phone unusable. Eek?! Anyone have a fix for this or any insight?
Thank you kindly,

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