There are a few versions of that motherboard out there, but generally yes, H67 chipset is capable of running a 3rd gen processor. However, that board was released with 2nd generation Intel CPUs, so a BIOS update with an older CPU installed may be necessary.
GPUs are pretty universal, particularly with OEM boards.
Yes, Windows 10 will run on it. There may be minor installation difficulties though, it might be best to start with an older OS and upgrade.