Can I install PC version of Need For Speed on my laptop and play it with Xbox 360 controller connected to my laptop? If yes, how?

You will probably need to download the xbox 360 drivers, if a wireless controller you may need a reciever but once you have got it to show up in the game controllers control panel configure your game to suit your desire.

If you bought the game on STEAM or the other PC gaming services, and already have it installed on your home computer, you can login to Steam on the laptop and install the game there as well. You can do this to as many computers you want, but will only be able to login to play on one at a time. I own the Wired USB Microsoft Xbox controller, and you are fully capable of plugging it into either your home computer or the laptop. I believe it's drivers are native to windows machines, so you shouldn't have to install anything, just plug and play. But there are some control features with the 360 button that I think a driver gives you better access to. And you can still use this Xbox controller on an Xbox.

Yup: Install it same way as normal (place disc in disc tray, click install and go through the wizard) Plugin your Xbox 360 Wired Controller and then map the key bindings to your controller. It does have to be a wired controller unless you're willing to buy a wireless adapter.

If you already have the Xbox controller for PC, you don't need to do anything other than installing the drivers. Just connect the controller and launch the game, it'll work.