PSU and everything is fine, open the case, and measure if 1070 fits in, if so you can. Zotac mini definitely fits. Should be fine.
the psu will be fine?, I don't know the actual wattage
The case is a normal size ATX case almost any GTX 1070 will physically fit. The system already has a GTX 1060 in it,t he motherboard can handle it no problem.
As for the PSU vapour is wrong, while the PSU in there is likely "500w" and in that case will "work" (you can confirm by opening the case and looking at the PSU label), however iBuypower is known for using low end PSUs in their system. If I were you I would purchase a better quality PSU with the GTX 1070, the Corsair CX550M should do the job and is priced well.