2. Will new card fit in tower. The GTX 1060 6.8 inch version graphics cards will fit. Some 1060 cards can be 10.5 inches or longer. You will have a problem installing these longer cards in your PC. EVGA makes a 6.8 inch card. You can also check Zotac, MSI, or Gigabyte brand cards.
3. Good power supply with a six-eight pin PCIE connector. You should have this on the HP 600 watt power supply.
You have windows 7 so UEFI Secure Boot is already disabled as Windows 7 cannot boot on a Secure Boot enabled BIOS.
Please uninstall all current Nvidia graphics drivers before replacing the graphics card. Make sure you run standard VGA graphics driver before add new card.