1) HDMI cable? donno if its for my MoBo, i've Z87 sabertooth and 4770k and haf932
An HDMI cable is well an HDMI cable. They are basically all the same
2) also the power pin cables the one you plug PSU to GPU by, donno if they're for the card
You mean a molex to PCI-E. Many GPUs will include this but with a decent PSU you don't need it.
3) and also there's sth between the monitor's cable (a blue thing) and the GPU (DVI to GPU?)
You mean VGA to DVI? Some GPUs include one incase you have an old monitor
4) there's a short cable with HDMI in one end and DVI to the other, (DVI to HDMI?)
Sounds like an HDMI to DVI