Will the GTX 1060 physically fit in my PC and can I link it to the gpu I already have?

Looking at the PC you posted, it seems like a standard ATX case. I can't say for sure though, because ASUS didn't give that information on their website.

The GTX 1060 will fit in a standard ATX case, as it can be expected to be as big as the 1070/1080. If you want to use both your GPUs for Gaming at the same time, they have to be of the same type and support SLI - in other words, you will have to replace the 760.