Yes, it will operate.
Yes, it will operate.
Yes, it is possible to activate PCs from a distance. Be cautious with your parents—they might worry if your computer turns on unexpectedly.
The Intel integrated graphics are decent these days, though Overwatch remains quite challenging. You should likely manage around 20-30 frames per second with everything set to low and a resolution of 720P. It may appear poor and still perform poorly, but it should run at all. EDIT: check the benchmarks for this GPU here (scroll down) https://www.notebookcheck.net/Intel-HD-G...576.0.html. That GPU struggles with most games; most get about 10fps at 720p low, while some less demanding titles work. I suspect Overwatch doesn’t fit that range.
Investigate thoroughly and test independently. It functions effectively.
I wouldn't bother either. It could only reach around 15 FPS at the lowest settings, which wouldn't be enjoyable or useful in a competitive shooter. You'd do better by exploring older titles or 2D indie games you enjoy. I've invested more time in Rimworld, Terraria, Shovel Knight, and FTL than most paid games I own.
You can't activate it, but you can bring it back to life by waking it from sleep. It can still receive updates and network data.