You don't have any HDRI picture for your world (or at least you haven't packed it) so the background is pink, remove the Environment Texture node from the World Shader Editor:
Back to Shader Editor > Object mode, plug the Image Texture into a Diffuse node, maybe load a lighter picture (the current one is 6144 px large)?
Create a sun in the scene, give it a Strength of 4 (just to check the result in Rendered preview mode). Select your anvil and switch it to Texture Paint, try to paint, if it still doesn't work, switch from a mode to another (From Material Preview to Solid) and then back to the mode you want (except Render preview). It should work.
For your last question:
- Choose Blend > Mix instead of Add
- Close the Texture Mask
- Keep the Texture if you want but in that case choose another color than black.