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Dozens of motherboard models are capable of supporting an Intel Pentium Dual-Core.
No, you cannot.
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Depending on its age, either SDR SDRAM, DDR, or DDR2 RAM.
Yes, depending on the motherboard. Most Pentium 4 chipsets support up to 4 GB of RAM, although the motherboard may not physically support enough RAM modules.
Yes. The Intel D945GNT motherboard supports dual-core Pentium D processors.
Yes. The GA-6BXC can support any Slot 1 Intel Pentium II or Pentium III processor. For the faster Pentium IIIs, you will need to purchase a "slotket" to convert a Socket 370 processor to the Slot 1 interface.
That would require purchasing a new motherboard, processor, and power supply.
The Intel P45SG can support up to eight gigabytes of memory across its four memory slots.
The CPU can be upgraded only if your motherboard/chipset and BIOS support it. Socket 478 motherboards cannot support a Dual-Core, as they use a different socket. If you have an LGA775 motherboard, it may work, but chipsets before 945 are not officially supported and may fail to function properly.
The processor is capable of addressing up to 4 GB of RAM. Chipset / motherboard limitations may make the possible max for a system less than that.
None, other than that you can get a Pentium I computer for about $5.