Well blender supports applying images as textures only using uv unwrapping and then applying it around your model as a texture. Still if a bit of makeshifter will be fine then you can apply your image on a brush after going in vertex paint mode in blender from there you can increase your brush size go in a veiw when you can see on what you want to apply your texture, mask out all the other areas using a mask brush increase your brush size, increase strength to 1 and pain but make sure that you have applied subdivision modifier or multiresolution modifier(if any) otherwise blender will not able to make out vetices to apply your texture on.
In order to change your image into a normal map it is really easy, you will have to go on a layer where there is nothing accept a plane(you will have to add a plane mesh on layer) mesh added so you can focus on it, go into top veiw by pressing 7 on numpad(num 7), change your veiw to shading make and make sure that your engine is better to cycles or eevee), add a new material and add an image texture with image you want to convert, connect it to a color ramp and feed color ramp into height input of a bump node into displacement input of material output node. Now you will have to add a subdivision modifier change it to normal and apply it for getting some geometry, create a new image in uv grid and make it resolution same as you require for normal map, go to rendering panel on left side of your screen, there you will be able to find an option of baking change it to normal, add one more plane select both by pressing shift and selecting high poly mesh first and add new image texture you created and select it go to baking panel change it to normal and bake, if you get no uv coordinates error then just select both planes one by one go into edit mode press u and select project from veiw(bounds), and your normal map is ready to be used.
