It is not a simple question, and it is appalling that people who use computers do not understand the concept of algorithms: clear step-by-step instructions which make sense and do not conflict with each other. Computers cannot read between the lines, so people who need help using them should not have to either.
Anyway, here are the correct answers:
1) Yes.
2) Choose the newest one that applies to your computer motherboard's chipset.
This is a quote from
http://www.intel.com/support/graphics/intel945g/sb/CS-020791.htm?wapkw=intel+82945g+express+chipset
"The Intel® 82945G Express Chipset family is the display adapter component of the Intel® 945G Express Chipset. The Intel 82945G Express Chipset family, combined with the Intel® Graphics Media Accelerator driver, delivers output of high quality 2D/3D video and graphics to the display."
After reviewing the drivers' readme instructions both drivers you listed are designed for Intel 945G Express Chipsets. According to the Dell documentation, all GX620 computers have Intel 945G Express Chipsets. Since your computer is a GX620 and the 82945G Express Chipset family is the display component for its chipset, you can use the driver with this name.
Why the other driver is listed for 945G chipset without the word "express" is confusing since all GX620 chipsets are express. Maybe because the driver is older they thought the word wasn't necessary at the time, who knows.
Anyway, they both apply to your chipset, so use the latest one called "82945G Express Chipset family".
3) This video driver called "82945G Express Chipset family" has no relevance to your pci-express slot.
While the driver is for the integrated graphics card relating to your 82945G controller relating to your 945G Express chipset under the name of 82945G Express Chipset family which does happen to affect the pci-express slot the driver is not meant to control the pci-e graphics cards. The video drivers you listed have nothing to do with the pci-e slot or the video cards that go in this slot. There are separate altogether different drivers for the chipsets that may affect the pci-e slot.
In other words just forget about this question.