In XNA, I used SpriteBatch. Is there something partially comperable?
No. Direct3D is a low-level rendering system. It's job is not to make your life easier (like XNA); it's job is to provide a bare-bones interface to graphics hardware.
You do not "draw textures" in D3D. You draw triangles, which have textures mapped onto them with shaders. Two triangles form a rectangle or "quad" (short for quadrilateral), which is how you draw textures.
To do this in D3D, you need to fill a vertex buffer with the vertex positions and texture coordinates for the triangles you want to render. You will also need a (very simple) pair of shaders, vertex and pixel, which pass your positions and texture coordinates. Your pixel shader needs to use the texture coordinate it gets from the vertex shader to fetch from the texture. And that texture's color becomes the pixel shader output.
You use all of these, the two shaders, the texture, and the vertex buffer, to render.
Low-level isn't easy, and it's not meant to be.