which is good for production
They are both good. sklearn can be used in production as much as tensorflow.keras
which will give me better and faster response
I think that doesn't really depends on the libray, rather on the size of your models and of your datasets. That what really matters. Both modules can be used to create very optimized and fast models.
is there any issue with introducing dependency over other libraries for just 1 or 2 functionality
There are not issues in using sklearn and tensorflow.keras together. In the ML/Data Science world they are probably the two most common tools. No worries about that!
which has a better compatibility with other tools like tensorboard or libraries like matplotlib, seaborn etc.
Well, keras is now a branch of tensorflow (it's tensorflow.keras). The TensorBoard is designed specifically for it. Other than that, all other visualization libraries such as matplotlib and seaborn are perfectly compatible.
Final thoughts:
use sklearn and keras in sequence without problems, Data preprocessing steps can use a lot more libraries. Don't worry of using one more, especially if it's a very solid and popular one such as sklearn.
However, you might want to substitute PCA with Autoencoders. That's arguably the best dimensionality reduction technique, it's non-linear, meaning it can carry more information with less variables, and it can be implemented in tensorflow.keras. In that way you'd have a neural network that generates a compressed representation of your data, and another that makes the prediction. That's just a suggestion of course, you know your task better than anyone else.