Handling libraries

It ultimately comes down to the library and the way it is setup. In that particular case, no, as SFML is built over OpenGL. OpenGL and DirectX aren't compatible. Some libraries are a bit more self contained and easily slotted into your setup, so you can use a portion of the functionality provided. DirectX and OpenGL aren't such libraries.

It would kind of defeat the purpose of SFML to support multiple platforms if they used a graphics library that is designed to only work with Windows, so no.

If you -really- need DirectX you'll have to look elsewhere or go and pretty much mutilate SFML to get it working correctly with DirectX, but honestly it's worth being familiar with both DirectX and OpenGL anyway.

The question is a bit similar to this: "Hi, I have this fantastic motorbike, but now I saw that other motorbike, can I ride both at the same time?"

You could try but it will most likely not end well, better just choose one and maybe use the other later for something else.

Generally the larger frameworks won't work well with others. Like someone already said, OpenGL and DirectX won't work well together.

First, you'll want to choose a framework to start with, probably something OpenGL or DirectX based, like SFML and others. Once you know which of those you will use, you can find solutions to particular problems. For example, if you want a way to create a menu in a certain way, it would be better to search for a way to do it in your framework and possibly find some open source code out there that does what you need.

Better to stick with one and learn the ins and outs to get what you need done.

Here's another question along the same line:

How would someone know this going into things? What questions would they ask? What should they look at?