You've hit on quite a complex area, but to quickly summarise:
Multi core processors tend to improve multi-tasking and some software can benefit from them as well. Multi core processors are here to stay for a long time to come. As software is released, it is (hopefully!) written to utilise the latest and greatest technology, which means that single core processors will soon be incapable of running latest software.
There are a number of comparisons done between DDR2 and DDR3. Most of these tend to lean on specfic uses though. E.g. gaming or data processing or AV scans. DDR4 is due for release next year, so DDR2 will likely quite quickly be phased out of new PCs when that happens.
DDR3 doesn't give massive performance upgrades in most cases, but DDR3 prices are not that far different from DDR2, so you might as well use it. Unfortunately that doesn't mean that shops don't charge a premium for DDR3 though.
No, a dedicated video card may not be much benefit, but it also depends on the onboard graphics that the motherboard has. Need more specific info to give a firm answer.
The upshot is this: define the use for the new PC (which you've done), define your budget and then find the best PC for the money.