Graphics card question

Nope you'll be fine with newer cards

No. GDDR is the extra virtual RAM the graphics card provides. It's a part of the graphics card, only used by the graphics card and therefore not directly linked to the motherboard (however, the card itself has to fit upon the motherboard).
The DDR motherboard specification is only important for the RAM sticks you can put into the motherboard's slots.

Graphics card have their own memory controller so mo matters what memory your motherboard support, but you'll have to check is the pcie bus available in your motherboard is enough for that graphics card and if your CPU will be able to max out the graphics card so you don't waste your money.

Graphics cards manage their own memory, it is completely independent from what you have on your motherboard. If you want to worry about something that should be the power supply and the PCIe rate (to a lesser extent).

https://forums.tomshardware.com/threads/1050ti-compatibility-with-my-motherboard.2930176/

You might want to change your mobo, so you can get a good (recent) cpu as well. Trust me, a good gpu with a bad cpu might be good in the beginning, because it's gonna be much better than what you had, but the more time passes, the more annoyed you get because of how much of your nice gpu is going to waste and how much you just can't do (or play) because the rest of the pc won't allow you to. I personally recommend going for a b350 amd mobo and any cpu from the ryzen series.

Careful though, your gpu might be bottlenecked by the cpu if it's too weak

Others have answered the memory question, but the motherboard compatibility is only tied to your PC's RAM, not your video card's VRAM.

DirectX 12 support is tied to the video card. If your video card supports it, and you're running Windows 10, then you'll have access to it. Do note that most games currently run faster on Nvidia cards on DirectX 11, particularly on the 10xx cards.

Dont worry. You can use any graphics card even 2080 Ti. The bottleneck is your old system. but any card will be working

the graphic card just need to have PCI Express x16 to work (and get sufficient PSU). DirectX will be based on graphics card, not mobo (the one listed for mobo is for integrated graphics)

As everyone else says any pcie card will work fine. Try to get one with more vram vs less. A great vidio processor with little vram just wont work very well in the future. I'd personally suggest 4gb as a minimum. It is relative to the games you play or want to play though. Research and reviews of different cards is your friend here.

Forget GPU upgrade. An i3-2100 is too weak for even a GTX 1050 Ti: https://www.youtube.com/watch?v=EWd5hlIl-WM | https://www.youtube.com/watch?v=hhWLlF_tdj0
Stay on that rig and get enough money to buy a completely new one.

If you want something that lasts for an acceptable price, then get ready to join Team Red, since currently the AMD Ryzen 5 2600 CPU and the AMD RX 580 GPU have the best price/performance ratio on the market in the middle segment price range…

The GeForce 1600 family is expected to be released soon. The 1660 Ti should be out any day now, but the 1660 and 1650 are also expected by end of next month. (Though NVIDIA hasn't announced anything yet.)

That would affect performance / price for low end cards. Might be worth waiting for it.