Is your old computer a brand name one (Dell, HP, etc)? If yes, then probably the answer is no. You will have problems with drivers.
If the computer is home build, then yes but you need the drivers for the new motherboard and might have to re-activate windows. The best thing to do is to re-install windows and all the drivers.
depends on hdd type, as well as if your going to use it as a boot drive. if you want the windows from it and if it was oem, it will not accept the new mobo unless you have a retail version which costs more.