Hi I'm new in these field.
I'm trying to put a fan(the RM19.90 gold colour round fan sold in IT Hypermarket) into a Geforce2 MX400 whos fan can't spin anymore.

Apparently the fan I bought is attached to the heatspreader, and the graphic card's heatspreader is like permanently glued to the processor.

So I have to put the fan with the heatspreader on top of the processor's heatspreader? If I do so I need some thermal grease right? Do computer shops sell them?
Or is there some way I could remove the processor's heatspreader?

Yes, computer shop sell thermal grease. One of them is Sri com.