Is there any theoretically proven optimal compression algorithm? Is Huffman coding always optimal since it uses Shanon's ideas?
What about text, image, video, ... compression?

Is this subject still active in the field? What classical or modern references should I read?
Huffman coding is optimal for a symbol-to-symbol coding where the probabilities of every symbol are independent and known before-hand. However, when these conditions are not satisfied (as in image, video), other coding techniques such as LZW, JPEG, etc. are used. For more details, you can go through the book "Introduction to Data Compression" by Khalid Sayood.