The first error you posted I'm pretty sure is coming from Tensorflow. You will see this error when Tensorflow tries to load CUDA dlls and either CUDA isnt installed or the wrong version of CUDA or CuDNN is installed. Could you post exactly how you installed Tensorflow? If it is being installed with a requirements.txt file, look in there and see if the tensorflow line is "tensorflow" or "tensorflow-gpu". If the gpu version is being installed then if will look for CUDA dlls even if the model you are using is being run on the CPU. If you are using a requirements file, one solution is to reinstall everything but remove the "-gpu" from that line. You could also uninstall tensorflow and install the CPU version. From a command line, run:
pip uninstall tensorflow-gpu
pip install tensorflow
Or if you are using Conda, you can install it with:
conda install tensorflow
Note: if you install tensorflow-gpu with Conda, it will automatically install CUDA toolkit and CuDNN for you. This should work whether you run your model on the CPU or the GPU.
As for the second error, I am not entirely sure, but I have a feeling that with a properly installed tensorflow in the arcGIS Pro environment this error might go away. I will look into this a bit more.