Simple answer, no. The i5-3570k is a desktop processor, not compatible in a laptop configuration. Long answer, the laptop's processor is soldered to the motherboard, so even the act of removing it will most likely lead to a broken machine. Really, the only parts that a user with moderate technical ability will want to replace is the memory and the hard drive. Swapping the hard drive with an SSD will make a huge difference, as will a memory upgrade. If you NEED a processor upgrade, you'll want to look at a complete new machine.
You should get an answer from the laptop manufacture. Socket should be the same, if there is one. E. Larson may be correct, but manufactures do strange things, a few years ago Toshiba used some (pre-i series) desktop processors. Even if it does work, clock speed and memory configuration may make it no better than the i3. Can you change the clock speed (bios)? More memory can help, but faster memory needs clock support. The SSD could be disappointing, the computer may not handle the faster i/o. In short, one chip, processor or no, may not do be the answer for your needs. Finally, what is your NEED? If it is graphic editing, you may need to design your own on a manufacturers sight - standard modern screens are designed only for games, cell-phone cameras and video. The manufacturers have never heard of a real digital camera, but some will provide vertical pixels at extra cost.
Most probably not! Laptops use lower power CPUs, that end in a S, T, or M. A laptop probably would not have the power or cooling for it. I would run the utility CPU-Z found at www.CPUID.com just to see what your existing CPU is. Also your laptop probalby does not have a 1155 socket, and even if it does, its BIOS may not recognise a desktop CPU. Suggest you purchase a new laptop with a I7- processor and a Graphic Chip.
In addition to the previous answers, I would like to mention that this processor is Ivy Bridge, which only came out within the last 9 months. I would guess that if you are looking to upgrade, your laptop is most likely older than that, and you would be using a Sandy Bridge setup.
For anyone buying a laptop, the only things you can reasonably expect to upgrade are the RAM and go from a mechanical hard drive to an SSD.