PwFClockWise

I think frob summarized everything well. If you would like to learn about DirectX and/or OpenGL this guy is presenting easy-to-digest-tutorials in my opinion: http://www.rastertek.com/tutindex.html 

I've followed these a few times myself and there haven't been a problem at all so far. The tutorials are built upon each other so you are wise to start at the very first lesson ^^! Good luck

Well, it all depends. You need to ask yourself: Do I want to make a game now or do I want to make a game later? Making your own engine will teach you a lot of low level code - which can be very useful and fun! But it will also take you a lot longer to finish a game. There is no right or wrong answer, do what you feel is the most fun right now and no matter what you decide you will gain valuable experience.

As previously said DirectX and OpenGL are not 2D libraries even if they can be used to for 2D rendering. SFML is something I've worked with, but only during 2 months or so. Me and some friends did a 2D game with it in college last autumn and it was pretty easy to work with. On the other hand I've programmed C++ for 3 years prior to this, so dunno how well you can code and if you can manage SFML.

When I started my first year in college we instantly started with C++ and after 6 months or so we were introduced to a 2D engine called HGE. We used that to make a simple(very simple) game for mobiles. It was 3 years ago so I'm not sure how I would feel about HGE now when I know a lot more, but I remember HGE being pretty easy to use - even as a beginner. But then again, programming was generally confusing at that time so maybe HGE isn't good at all ^^!

Might be worth checking up on, though. If HGE turns out to be too confusing I would really recommend SFML due to its helpful community and its broad usage.
 

HGE: http://hge.relishgames.com/ There are some example games posted on this link as well, might be interesting to check them out as well.

Good luck coding!

I haven't learned any DX9 since DX10 was available when I started studying the subject. I don't know how much the DX9 differs from DX10, but the difference between DX10 and DX11 isn't big at all. I had no problems what so ever to switch to DX11, so in that regard I don't think there would be too hard for you to switch from DX9 to DX11 when you can.

But, then again, I don't know how much DX9 differs from DX10. Hopefully this was of any use to you

Well, I also had a computer that did not support the DirectX11, and the only thing I had to change was this line: D3D11CreateDeviceAndSwapChain(NULL, D3D_DRIVER_TYPE_HARDWARE, NULL, 0, &featureLevel, 1, D3D11_SDK_VERSION, &swapChainDesc, &m_swapChain, &m_device, NULL, &m_deviceContext);

To this instead: D3D11CreateDeviceAndSwapChain(NULL, D3D_DRIVER_TYPE_REFERENCE, NULL, 0, &featureLevel, 1, D3D11_SDK_VERSION, &swapChainDesc, &m_swapChain, &m_device, NULL, &m_deviceContext);

This will allow you to do everything in DirectX11, but will use the CPU to draw instead of the Graphics Hardware. Obviously this will lower your FPS by like a 1000 times, so you will have like 0.1 fps or something. But it will work ^^