"845G" is a chipset, not a processor. The chipset is actually a part of the motherboard, and should be advertised in it's specs.
This is a very old graphics chipset, and no longer supported by Intel, except for downloads of existing drivers. No drivers were ever made for Windows Vista for it. You may be able to install the Windows XP drivers, but since the card is very old and doesn't support any real form of hardware acceleration, there is no advantage to using it over Vista's built-in generic VESA driver.
That depends on the chipset the motherboard uses. 865P, 850E, 845PE, 845GE, 845GV, 845E, and 845G chipsets will all work with a hyperthreading Pentium 4 (a BIOS update may be required to support hyperthreading capabilities). Older chipsets like the original 845 and 850 won't work.
a chipset is a set of chips on the motherboard that collectively control the memory, buses on the motherboard, and some peripherals. High-performances chipsets-the X58bchipset supports the Intel LGA1366scoket Mainstream desktop chipsets-The P45,P43,P35,G45 and G31 chipset supports Core 2 Quad and Core 2 Duo Intel processers. Value desktop-The 910GL,845E,845G chipset supports the Pentium 4,Celeron,and Celeron, and Celeron D processors in low-end systems. Older value desktops-the 845 and 845GL chipset support the Pentium 4 or Celeron processeor in a low-end system using the 478PGA socket