At the time of writing this (11/21/2009) it's the ATI HD4670 which is available in AGP 8x format will function perfectly fine in an AGP-4x motherboard.
Yes, at 4x speed.
There is no 4X AGP Graphics card that has 256MB but only 128MB that's called the Nvidia Geforce4 Ti4600
Yes, it should do, but only at 4X. The video card (and it's drivers) ought to recognise the AGP's speed and will operate accordingly.
http://cgi.ebay.co.uk/NVIDIA-GeForce-FX5500-256MB-AGP-8x-4x-Video-card-5500_W0QQitemZ190257585474QQcmdZViewItem?hash=item190257585474&_trkparms=72%3A1300%7C39%3A1%7C66%3A2%7C65%3A12%7C240%3A1318&_trksid=p3286.c0.m14 ^^ Is a 256mb graphics card that supports 4x and 8x AGP. One of the only cards above 64mb that I've ever seen that supports AGP 4x. http://cgi.ebay.co.uk/NVIDIA-GeForce-FX5500-256MB-AGP-8x-4x-Video-card-5500_W0QQitemZ190257585474QQcmdZViewItem?hash=item190257585474&_trkparms=72%3A1300%7C39%3A1%7C66%3A2%7C65%3A12%7C240%3A1318&_trksid=p3286.c0.m14 ^^ Is a 256mb graphics card that supports 4x and 8x AGP. One of the only cards above 64mb that I've ever seen that supports AGP 4x.
Any 4x or 8x AGP card.
Yes, AGP is completely backwards compatible.
Yes, but the card will only register at 4x AGP. You will not get the most out of the card with that mobo, but will still have great results.
AnswerYes.Added:Sometimes! Not all AGP 1x or 2x video cards will have the same connection type as 4x or 8x cards, some older cards will not physically fit in the slot for modern motherboards.
No. They are totally different on an electrical, physical, and protocol level. Attempting to insert a PCI-E card into an AGP slot, or vice versa, will likely damage both the motherboard and the card.
No it won't work!
Bandwidth.
You need an older AGP card. The newer PCI-E cards won't work. You can get a 4x or an 8X AGP card. There is no such thing as 'size'. But you can get various amounts of memory in the AGP card, like 32MB or 64MB, or maybe even 128MB. ANy amount of memory will work (to varying degrees) as long as they are AGP cards.