1. You have ATA 6(IDE) ,so max bandwidth is 133MBPS.so,it should be ok.But please avoid ide to sata converter at all costs.as they work at different voltage levels and therefore you would need to give power(from smps) to your converter.And they don't work always.

2. PCI 2.2 specs about your mobo can't be found out.
But from the least values known,it is 133MBPS(worst case)
But I am guessing since your bus is 64bit,it may be 264MBPS!
either way you are on higher side of what the newer HDDs can offer.
I hope you are not using any other PCI device.(saw that you have AGP gfx card)as,lesser devices mean better efficiency.
I think PCI-to sata card is the best option(price maybe around 200-300,dunno exactly but definitely less than 500).

3.viruswin32 hasn't posted the pc spec on which he did the ide-to-sata converter speed tests.
But RAM usage in your computer is already 92%,so Iam not sure whether you would touch the max speeds of WDC 1TB Green..
but you are already getting average 45MBytes per second(with your old HDD) as per HDTach results(correct me if it is not the case)

3.No point of external HDDs for any desktop.They should be bought ONLY if you need mobility.

4.you may keep your old HDD as OS drive itself.
As you don't need speed for any data-intensive jobs.keeping 1tb as Storage only would help preserve it's life.
also,backup sensitive data (i.e., keep on both drives)
and if and when old one fails,,you can ask for a sata replacement.And you would have a faster and fatter HDD than your old HDD.
P.S.-Most pci to sata cards come with 2 internal sata ports(DO CHECK,still) and one external e-sata port.so you needn't worry about it in the future when you get replacement for your old seagate
To sum et all:
1.Buy pci-sata card
2.Buy 1TB WDC Green
3.