The case is an ATX case and the motherboard is ATX - these will fit fine.
Here are the dimensions of the heatsink: Approximately 6 1/4" high (from where it touches the CPU to the top of the tower); approximately 5 1/4" wide; and approximately 4 1/2" deep. It will fit in the Full Tower Case you have selected. If you have memory with a tall heatsink, you will not be able to use it in the first 2 slots closest to the CPU socket, but memory with regular heatsinks fit fine.
The brackets supplied for socket 1156, may be suitable for socket 1155 (Sandy Bridge), even though this is not stated in Tuniq's specs. - Verify this by calling Tuniq's tech support.