Can you give us some examples about the lack of the theoretical justification in deep learning!!??

I disagree with your point regarding " lack of theoretical justification " . There are very good papers with nice theory behind them. Here's some answers:

Q1) So what is the lower threshold for the overall size of data to be tested via deep learning algorithm for training, validation and testing?

A: It depends on the task and the capacity of the network. There is no general answer to this.

Q2) In comparison to the conventional pattern recognition algorithms how it works differently? Give examples?

Conventional pattern recognition algorithm are mainly not data-driven. As such, most of them don't require annotated datasets. In image segmentation for instance, you may need user interaction to initialize an active contour.

Q3) What configuration of CPU/GPU is necessary and sufficient requirement for processing data via deep learning algorithm?

A: You may want to take a look at these:

https://timdettmers.com/2019/04/03/which-gpu-for-deep-learning/

https://blog.inten.to/cpu-hardware-for-deep-learning-b91f53cb18af

Q4) Any examples of various tasks via deep learning using MATLAB?

A: MATLAB is not the best choice for deep learning, since it is a scripted language and lack many features that general frameworks such as Tensorflow and Pytorch offer.

MATLAB supports some deep neural networks such as CNN and LSTM since MATLAB 2018B. MATLAB has some functions for you to build deep neural networks, which is a little similar to Keras. You can refer to the official guidelines of MATLAB. However, I still recommend you to learn some open-source Python libraries such as Tensorflow, Pytorch and Keras for deep learning