Personally, I don't give over any computing device to a third party. However, it does require you figure out how to fix it yourself, or recover data. No easy way to choose between trusted third party and time spent learning to DIY hardware.
For intermittent problems, it could be heat related: Check fans all operating properly (especially on the CPU and GPU), no dust buildup, and computer itself has plenty of breathing room around it.
A screen blackout could be graphics card: If you are able, switch out the graphics card with another.
PC tech support can sometimes be trial and error swapping if you don't have monitoring tools.
And I know that feeling... wondering if there's a security hole or oversight. That's good you have that fear, because if you didn't, you'd be a whole lot more vulnerable. Hope all works out ok.
I would have looked at it too before, but I struggle with these kinds of things now. This PC I bought rather than building myself, because of the challenges I have with that kind of learning. I am not "not" technical, but not as technical as I once was :)
Wasn't heat and all PC components were performing well. Very strange.
Fear is good. Most people are scared of the wrong things.