It comes with a GTX 745, which is a 55W, PCIe power only GPU.
1. A 1060 is a 120W card at best.... so it won't be "enough". It won't have additional power connectors (as the 745 doesn't need it), and may not be of the best quality to begin with. Adding a 1060 to that system puts your max theoretical use from somewhere in the low 200W to near (or a little more than) 300W. Unless that comes with the best quality 300W PSU ever, which also has additional PCIe power connectors, you'll be replacing the PSU too.
2. Depends on the model & the inside layout of the case. A "Mini" variant (~5.7") is no bigger than the 745 so should fit for sure/