The programmer decides, which tasks will be performed on CPU, and which - on GPU. GPU is a full capability processor that runs its own program, so in theory there is no limit on what it can do - the only limit is time. The programmer must write a program for GPU as well as for CPU. Programs for GPU are called "shaders".

If we talk about games, the GPU usually does at least 3 jobs: convert all 3D models to screen-relative coordinates, sample colors from texture images, and calculate light and shadow. However, more tasks get moved on GPU with time: modern games use it for simple physics simulation (hair, clothes, fire, smoke, rain, grass), and for post-processing (color correction, blur).

GPU can also be used in tasks unrelated to graphics. Many scientific physics simulators and machine learning tools have an option to run on GPU.

No, not really. Modern browsers are pretty resilient, they generally don't trust the code on the page, and limit its possible actions. Loopholes still happen, but they get patched quickly. This is the first line of defense.

Then, they run the crawler code on a restricted user account, so the operating system will refuse any access to system files. That's the second line.

Finally, if the malicious code somehow finds a loophole in a browser, AND THEN a loophole in OS, they get to live - up until the next system wipe.

If the game has no anti-piracy protection - then it is exactly how it works: just copying files is enough.

If there is a protection - the game will try to check if you bought the game. However, the game runs on your computer, for which you have absolute control over! Yet.

• If the game checks DVD disk, you can install a fake DVD driver. It will pretend, that there are a disk installed and will allow a program to read it - but will actually read data from a file. Then just copy data from the real DVD to a file.
• You can inspect the program's memory to figure out what its doing, and then edit the EXE to change its behavior. Yes, it contains the dreaded "machine code", the language of the CPU - but it is possible to just learn it (it's description is published on the Internet). You can also use helpful tools, that will convert it into a more human-readable form. The goal is to find a place where the game does a check, and replace it with "always pass".

You don't need a table of squares. This method works, even if you don't start with a square. You just need to start as close as possible to the square root.

Even some crude approximation, like "closest power of 10", is enough for the initial value.

Most hackers don't hack one specific account: they try to get any account. So instead of trying many passwords on the same account, they try the same password on many accounts. And because accounts have separate lockout counters, they are not getting triggered.

Of course, good websites also count attempts per IP, but a hacker can buy a botnet (a lot of computers infected with a virus) to get a lot of disposable IPs.

When hackers target a specific account, they usually come prepared with a short list of possible passwords - which they could get by hacking the same person on a different website with bad security. That's why experts recommend you to never use the same password on several websites - if one of them get hacked, they'll come for all the others too.