This paper presents the first significant work on directly predicting 3D face landmarks on neural radiance fields (NeRFs), without using intermediate representations such as 2D images, depth maps, or point clouds. Our 3D coarse-to-fine Face Landmarks NeRF (FLNeRF) model efficiently samples from the NeRF on the whole face with individual facial features for accurate landmarks. To mitigate the limited number of facial expressions in the available data, local and non-linear NeRF warp is applied at facial features in fine scale to simulate large emotions range, including exaggerated facial expressions (e.g., cheek blowing, wide opening mouth, eye blinking), for training FLNeRF. With such expression augmentation, our model can predict 3D landmarks not limited to the 20 discrete expressions given in the data. Robust 3D NeRF facial landmarks contribute to many downstream tasks. As an example, we modify MoFaNeRF to enable high-quality face editing and swapping using face landmarks on NeRF, allowing more direct control and wider range of complex expressions. Experiments show that the improved model using landmarks achieves comparable to better results.