There is no hard "limit" to the amount of memory your external video card can have, so you should be able to use that GT210 with 1GB assuming you have drivers that work with the OS you have installed.
GPU memory ? You are talking about ASRock MB, it has a x16 PCIe slot so it should support any of new GPUs that being said its old 2006 release date I think so probably not worth it to put anything higher than a 1030 GT.
It would appear that your motherboard does not support integrated graphics so your question is moot.
The vram(gpu memory) will be whatever your discrete graphics card has.
I had a geforce 7300 LE that had 256mb vram and now its broken and I want to put in it a GT 210 that has 1GB vram until I'll get a new PC and I wanted to know if there is a limit of GPU vram memory on the motherboard.
There is no hard "limit" to the amount of memory your external video card can have, so you should be able to use that GT210 with 1GB assuming you have drivers that work with the OS you have installed.