Why can I only texture paint some parts of the model I am only able to paint some parts of the model but it just doesn't add any color to some other parts or the color it got added is very faint. Please see the red circled area in the screenshot. I am really confused about this. Can someone please let me know what I did wrong here? Thanks.

I also checked the UV unwrapping and all the normals associated to that area which seem okay.
In your first photo the reason why your texture looks so strange is because the UV associated with that face is squished in a way that it can only take the colour of a single row of pixels. A way to fix this is to select some of your edges and right click, then create seams. Then select everything and press U, then smart unwrap. This should be able to make your UV map easier to work with.